mm 


MODERN 
BUSINESS  ARlTHMtliC 

COMPLETE  COURSE 


FINNEY 

AND 

BROWN 


GIFT  OF 


p.^ 


MODERN   BUSINESS   ARITHMETIC 


COMPLETE   COURSE 


BY 
HARRY   ANSON   FINNEY 

LECTURER   IN    ACCOUNTING,    WALTON    SCHOOL    OF   COMMERCE 
CHICAGO,    ILLINOIS 

AND 

JOSEPH   CLIFTON   BROWN 

PRESIDENT,    STATE   NORMAL   SCHOOL,    ST.    CLOUD,    MINN. 


LMMJV.      •'':> 


di^^-j^^ 

NEW  YORK 

HC 

)LT   AND 

COMPANY 

BY 

HENRY  HOLT  AND  COMPANY 


PREFACE 

This  book  provides  a  year's  work  in  the  arithmetic  of  modern 
business.  All  topics  which  have  no  reason  for  inclusion  except 
tradition  have  been  omitted.  Topics  which  have  recently  acquired 
importance  because  of  changes  that  have  been  brought  about  in 
the  organization  and  conduct  of  business  are  included.  Among 
the  topics  so  included  are  Contract  Purchases  and  Installment 
Payments,  Depreciation,  Advertising,  Insolvency  and  Bankruptcy, 
Comparative  Statistics  to  Promote  Buying  and  Selling  Efficiency, 
Profit  and  Loss  by  Departments,  Finding  the  Profit  and  Loss  on 
Each  Sale,  Factory  Costs,  Tabulations  for  the  Sales  Manager,  and 
the  Income  Tax. 

The  illustrations  and  model  forms  were  chosen  with  a  view  to 
acquainting  the  student  with  actual  business  conditions.  The 
problems  were  selected  from  those  which  actually  arise  in  impor- 
tant business  activities,  and  the  methods  of  solution  are  those 
which  are  used  in  business  practice.  Many  of  the  drill  exercises 
are  put  into  ruled  forms  such  as  will  be  met  in  the  business  world; 
and  the  student  is  given  practice  in  the  art  of  presenting  business 
statistics  and  other  material  in  a  neat,  concise,  and  attractive 
manner.  The  traditional  sequence  of  topics  has  been  abandoned 
in  some  cases  in  favor  of  a  grouping  of  topics  in  which  there  is  a 
relation  of  business  experience. 

The  necessity  for  a  high  degree  of  accuracy  and  facility  in 
arithmetical  computation  has  been  fully  recognized.  Abundant 
material  for  practice  and  drill  in  the  fundamental  processes  is  pro- 
vided. The  student  is  required  to  check  his  results  at  every 
point  in  order  to  secure  accuracy;  and  numerous  exercises  to  be 
finished  within  a  time  limit   are  included  to  improve  speed  in 


IV  PREFACE 

computation.  Since  business  expediency  demands  that  many- 
problems  shall  be  solved  orally,  a  large  amount  of  oral  work  has 
been  included. 

From  the  point  of  view  of  both  material  and  method  this  book 
is  based  not  on  theory  but  on  actual  business  conditions  and 
practices.  The  material  has  been  successfully  subjected  to  the 
test  of  preparing  hundreds  of  students  to  meet  the  exacting 
demands  of  the  business  world.  The  ruled  forms  and  the  tabu- 
lated business  statistics  so  extensively  used  in  the  book  have 
demonstrated  their  effectiveness  in  developing  rapidity,  accuracy, 
and  neatness.  Many  men  who  are  specialists  in  various  business 
and  industrial  activities  were  consulted,  and  the  statements  of 
business  customs  as  well  as  the  tabulation  of  materials  and  the 
arrangement  of  problems  are  based  on  their  advice. 

The  authors  wish  to  acknowledge  their  indebtedness  to  the 
numerous  teachers,  business  men,  and  professional  men  who  have 
so  kindly  aided  them  by  offering  valuable  suggestions  and  dis- 
criminating criticisms,  and  by  furnishing  materials.  They 
acknowledge  especial  indebtedness  to :  Mr.  Seymour  Walton, 
Certified  Public  Accountant,  Dean  of  the  Walton  School  of  Com- 
merce, Chicago,  who  read  several  of  the  chapters,  the  subject 
matter  of  which  borders  on  accountancy;  Professor  Norris  A. 
Brisco,  head  of  the  School  of  Commerce  and  of  the  Departments 
of  Political  Economy  and  Sociology  in  the  University  of  Iowa  and 
Editor  of  the  Efficiency  Society  Journal ;  Mr.  Stanley  C.  Crafts, 
Auditor  of  Customs,  Port  of  Chicago ;  Mr.  T.  H.  Fuller,  Auditor 
for  Carson,  Pirie,  Scott  &  Co.,  Chicago  ;  Mr.  H.  A.  Brinkman, 
Cashier  of  the  Harris  Trust  and  Savings  Bank,  Chicago  ;  and 
Mr.  H.  V.  Church,  Principal  of  the  Cicero  Township  High 
School,  Berwyn,  111. 

HARRY  ANSON  FINNEY. 
JOSEPH  CLIFTON  BROWN. 


CONTENTS 


FUNDAMENTAL  PBOC ESSES 

mAPTEB  PAGE 

I.     Addition 2 

II.     Subtraction 16 

III.  Multiplication        .         . .24 

IV.  Division 39 

V.     Average 48 

VI.     Factors  and  Multiples „  55 

VII.     Common  Fractions 59 

VIII.     Decimal  Fractions 73 

IX.     Short  Methods  Involving  Aliquot  Parts 85 

UNITS   OF  MEASURE  AND    THE  IB  APPLICATIONS 

X.     Denominate  Numbers     .         . .94 

XI.     The  Metric  System 103 

XII.     Practical  Business  Measurements 112 

XIII.  Drawings  and  Graphs 137 

PERCENTAGE 

XIV.  Percentage 152 

TRADING  ACTIVITIES:   PROFIT  AND  LOSS 

XV.     Buying  and  Selling  Merchandise       ......  176 

XVI.     Commercial  Discounts .         .  183 

XVII.     Recording  Purchases  and  Sales          ....,,  196 

XVIII.     Paying  for  Goods 206 

XIX.     Collecting  Bills 225 

XX.     Foreign  Money  and  Exchange .  233 

XXI.     Accounts .  245 

XXII.     Taking  Inventory 249 

XXIII.     Gross  Trading  Profit 255 

V 


VI 


CONTENTS 


BORROWING  AND  LOANING 

CHAPTER  TAQK 

XXIV.  Interest 257 

XXV.  Partial  Payments 274 

XXVI.  Compound  Interest 279 

XXVII.  Savings  Banks 282 

XXVIII.  Contract  Purchases  and  Installment  Payments  .         .         .  288 

XXIX.  Discounting  Notes  and  Other  Commercial  Paper        .        .  291 


BUSINESS  EXPENSES 

XXX.     Wages  and  Payrolls          . 303 

XXXI.     Postage,  Freight,  and  Express  Rates 311 

XXXII.     Depreciation 323 

XXXIII.  Advertising 327 

XXXIV.  Property  Insurance 333 

XXXV.     Taxation 345 

XXXVI.     The  Income  Tax 351 

XXXVII.     Customs  Duties 351 

BUSINESS   ORGANIZATION 

XXXVIII.     Individual  Proprietorship .362 

XXXIX.     Partnership 368 

XL.     Insolvency  and  Bankruptcy 378 

XLI.     Corporations,  Stocks,  and  Bonds 381 

TABULATIONS   TO  PROMOTE  EFFICIENT  MANAGEMENT 

XLII.     Buying  Expenses  ;   Selling  Expenses  ;   Net  Profit        .         .  398 

XLIII.     Finding  the  Profitable  Departments 411 

XLIV.     Finding  the  Profit  or  Loss  on  Each  Sale     ....  416 

XLV.     Factory  Costs 421 

XL VI.    Tabulations  for  the  Sales  Manager 438 

MISCELLANEOUS 

XL VII.    Consignments  and  Commissions 452 

XL VIII.     Life  Insurance 458 

XLIX.     Farm  Records     . 464 

APPENDIX .477 

INDEX 483 


INTRODUCTION 

To  the  Student 

If  you  expect  to  succeed  in  the  business  world,  you  should 
cultivate  accuracy,  neatness,  and  speed  in  all  computations.  A 
high  degree  of  accuracy  is  indispensable.  Be  very  careful  about 
all  of  your  work,  and  use  adequate  means  of  checking  your  results. 

Take  pride  in  the  appearance  of  your  work.  Your  papers  from 
day  to  day  should  be  prepared  with  ink,  because  that  is  the  way 
business  records  are  kept.  When  ruling  is  to  be  done,  make  the 
lines  fine.  Make  your  figures  small  and  similar  to  those  in  the 
following  model : 

/    ^     3     ¥    S    6     J    S     f    O 

Work  as  rapidly  as  you  can  without  detriment  to  your  accuracy. 
The  material  in  this  book  has  been  prepared  with  the  special 
purpose  of  making  students  accurate,  careful,  and  rapid  business 
workers. 


FUNDAMENTAL  PROCESSES 

CHAPTER  I 

ADDITION 

1.  Drill  Tables.  The  following  table  contains  the  forty -five 
combinations  of  two  numbers,  each  of  which  is  less  than  ten. 
Practice  until  you  can  state  these  forty-five  sums,  without  error, 
in  less  than  twenty-five  seconds.  Do  not  repeat  the  numbers  to 
be  added.     State  results  only. 

264617472233121 
98492769   5   456185 


7 

1 

8 

5 

4 

8 

2 

3 

4 

5 

2 

1 

5 

9 

4 

8 

4 

8 

9 

5 

9 

3 

4 

9 

5 

7 

3 

6 

9 

7 

1 

6 

3 

6 

1 

3 

1 

5 

2 

3 

5 

1 

2 

4 

3 

9 

7 

3 

6 

7 

8 

8 

7 

2 

9 

8 

6 

6 

8 

7 

The  following  group  of  thirty-six  combinations  contains  all  the 
inversions  possible,  omitting  the  pairs  of  equal  numbers.  Prac- 
tice until  you  can  state  the  sums  in  any  order  without  hesitation. 


4 

7 

9 

2 

6 

3 

6 

8 

7 

4 

7 

8 

3 

5 

5 

1 

5 

1 

1 

5 

4 

1 

6 

3 

7 

4 

7 

8 

9 

8 

9 

9 

5 

6 

9 

8 

1 

2 

2 

4 

3 

6 

7 

2 

2 

4 

4 

7 

9 

8 

9 

3 

9 

8 

6 

5 

7 

5 

5 

6 

8 

1 

6 

2 

1 

2 

3 

4 

3 

1 

3 

2 

ADDITION  3 

Following  are  the  eighty-one  combinations,  including  inversions, 
of  two  numbers,  each  of  which  is  less  than  ten.  Practice  on  this 
exercise  until  you  can  state  the  sums  in  less  than  a  minute. 


1 

3 

2 

4 

6 

4 

7 

3 

2 

9 

1 

8 

3 

2 

6 

8 

8 

2 
1 

1 

8 

1 

9 

8 
6 

4 
5 

8 
5 

6 

7 

4 

7 

8 
9 

9 

8 

5 

6 

3 
9 

7 
7 

8 
8 

4 

8 

9 
4 

3 

7 

7 
6 

2 
9 

9 
1 

1 

2 

3 
4 

9 
5 

8 

7 

9 
3 

1 

7 

6 
5 

9 
2 

2 
6 

4 

9 

5 

7 

8 

2 

6 

8 

6 
9 

42762887321291775 

6842569517373 
3425149345521 


The  following  exercise  contains  the  nine  digits  in  groups  of 
three.  Practice  on  these  combinations  until  you  can  state  the 
sums  in  less  than  two  and  a  half  minutes. 

887584589675446854 
683532567553343243 
223222332332333222 


3  5  3664576978679866 
223364474827232765 
222222.4  23222222134 

789898779968798957 
786548454353694854 
332321223223212344 


4  ADDITION 

889997599897889676 
469364368867575476 

667899987899579989 
467777556878468859 
446457355765336828 

798999778898999878 
566959654698574767 
£5^^^!5i51f?1^4344 

899896997899 
79867  5  697887 
56764563  5  543 


Oral  Work 

Add  the  following.  In  this,  and  in  all  other  work  in  addition, 
name  the  sums  only.  For  example,  in  adding  3,  4,  7,  9,  say  7, 
14,  23. 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

14. 

15. 

16. 

3 

5 

7 

2 

9 

1 

6 

8 

5 

4 

9 

3 

5 

5 

7 

9 

7 

3 

9 

1 

5 

3 

7 

5 

6 

9 

8 

9 

3 

9 

3 

8 

2 

8 

3 

5 

7 

1 

4 

9 

6 

4 

6 

7 

9 

4 

9 

3 

6 

3 

8 

1 

4 

2 

7 

8 

9 

6 

7 

8 

7 

8 

2 

7 

6 

3 

7 

5 

2 

9 

5 

1 

7 

4 

8 

4 

1 

9 

8 

5 

7 

8 

5 

3 

9 

1 

4 

7 

6 

4 

3 

9 

8 

7 

9 

9 

8 

4 

9 

5 

7 

3 

5 

8 

5 

9 

9 

6 

9 

8 

9 

8 

9 

2 

5 

3 

7 

4 

8 

5 

9 

6 

6 

1 

6 

3 

5 

6 

Name  the  sums  in  each  of  the  following.  The  first  two  num- 
bers in  each  example  should  be  thought  of  as  one  number.  Thus, 
in  the  first  example,  think  10,  17. 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12 

13. 

14. 

7 

5 

9 

1 

2 

5 

8 

2 

4 

6 

3 

7 

5 

9 

2 

4 

1 

6 

7 

4 

1 

7 

3 

2 

8 

4 

3 

9 

8 

4 

6 

9 

2 

9 

5 

7 

3 

8 

5 

3 

7 

5 

ADDITION 


15. 

8 
6 
4 


16.  17.  18.   19.  20.   21.   22.   23.   24.   25.   26.   27.   28. 


8  4 
8  5 
3   6 


29.  30.  31.  32.  33.  34.   35.   36.   37.   38.   39.   40.   41.  42. 

77495746836579 
673695  83674573 
74853738542694 


2.    Adding  numbers  by  grouping  will  increase  your  speed.     Most 
rapid  computers  use  group  addition.     For  example, 


4 
_2 
17 


6 


Use  this  method  to  find  the  sums  in  the  following  exercise. 
This  work  should  be  done  orally. 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

14 

6 

5 

8 

4 

7 

4 

8 

5 

2 

6 

3 

5 

4 

6 

3 

2 

2 

3 

4 

3 

6 

7 

3 

7 

7 

8 

9 

6 

5 

7 

3 

4 

8 

5 

3 

7 

5 

4 

9 

4 

7 

3 

4 

3 

6 

2 

3 

5 

7 

6 

4 

8 

4 

1 

3 

o 

15„ 

16. 

17. 

18. 

19. 

20. 

21. 

22. 

23. 

24. 

25. 

26. 

27. 

28 

3 

7 

4 

2 

5 

3 

6 

2 

4 

6 

8 

•9 

7 

5 

3 

6 

4 

8 

5 

3 

7 

6 

4 

8 

5 

7 

3 

6 

7 

5 

3 

6 

5 

8 

4 

5 

6 

4 

7 

3 

8 

2 

7 

6 

3 

4 

1 

7 

4 

7 

4 

8 

9 

5 

3 

7 

29. 

30. 

31. 

32. 

33. 

34. 

35. 

36 

37. 

38. 

39. 

40. 

41. 

42 

3 

2 

6 

8 

6 

4 

2 

4 

6 

4 

8 

5 

2 

3 

3 

6 

2 

5 

8 

9 

5 

3 

7 

5 

3 

5 

7 

9 

9 

5 

3 

6 

8 

9 

5 

2 

6 

2 

8 

5 

3 

9 

5 

2 

7 

4 

2 

7 

3 

7 

9 

4 

2 

7 

4 

6 

6  ADDITION 

43.    44.    45.    46.    47.    48.    49.    50.    51.    52.    53 

48953268436 
36842674368 
7463. 7  853679 
47528648379 
26479642675 
74839593675 


54. 

55. 

56. 

57. 

58. 

59. 

60. 

61. 

62. 

63. 

7 

3 

2 

8 

5 

3 

7 

3 

7 

5 

5 

3 

6 

8 

7 

4 

2 

6 

8 

3 

4 

5 

6 

4 

7 

3 

8 

4 

2 

8 

5 

2 

3 

5 

7 

8 

5 

3 

6 

7 

4 

7 

6 

4 

8 

9 

2 

6 

3 

7 

2 

3 

6 

7 

8 

4 

2 

5 

6 

3 

Find  the  sums  in  examples  1-14  by  the  following  method : 

43 

24        Think  43,  63,  67. 

67 

1.       2.       3.       4.       5.        6.        7.       8.       9.       10. 

24     46     37     53     58     67    48     39     68     73 

33     52     4463475973584286      ___      _      __ 

3.  Recording  Addition  by  Columns.  For  convenience  in  check- 
ing, the  total  of  each  column  may  be  recorded  separately.  This 
will  enable  you  to  resume  the  work  where  it  was  discontinued  if 
you  are  interrupted  after  having  added  one  or  more  columns. 
Three  slightly  different  methods  are  in  use. 


11. 

12. 

13. 

14 

66 

81 

93 

65 

59 

78 

38 

75 

a. 

h. 

c. 

369 

369 

369 

487 

487 

487 

352 

352 

352 

896 

896 

896 

294 

294 

294 

28 

20 

28 

37 

37 

39 

20 

28 

23 

2398  2398 


ADDITION  7 

Illustrations  (a)  and  (5)  show  the  method  of  adding  each 
column  without  carrying  the  tens.  The  column  totals  must 
be  added  to  obtain  the  final  result.  Illustration  ((?)  shows 
the  method  of  adding  to  each  column  the  amount  carried 
from  the  column  at  the  right. 

Written  Work 

Make  the  figures  plain  and  easily  legible  and  place  units  of  the 
same  order  in  the  same  vertical  column. 

Copy  and  find  the  sum  of : 


1. 

2. 

3. 

4. 

5. 

5823 

84239 

887935 

9328577 

88421 

4923 

42937 

512937 

4912374 

31238 

9382 

31629 

491327 

5823746 

312 

5128 

49238 

395825 

4923748 

273845 

3258 

83153 

416239 

7239482 

39547 

7362 

42841 

482423 

1423849 

815288 

8127 

52384 

923857 

8237421 

4234 

4239 

94856 

412831 

9423748 

21582 

6. 

7. 

8. 

9. 

10. 

11. 

27 

371 

419 

372 

97 

996 

83 

927 

82 

496 

86 

37 

95 

482 

92 

18 

547 

821 

84 

413 

412 

739 

969 

493 

82 

958 

892 

847 

38 

782 

15 

285 

9216 

96 

487 

946 

81   , 

381 

594 

882 

692 

531 

48 

294 

5 

75 

99 

28 

79 

148 

592 

989 

881 

327 

Each  student  should  prepare  original  examples  for  addition,  fol- 
lowing the  instruction  of  the  teacher.  Exchange  papers,  criticize 
the  form,  and  find  the  sums. 


8 


ADDITION 


The  ability  to  give  and  to  take  dictation  of  numbers  should  be 
developed.  Numbers  may  be  dictated  by  the  teacher,  or  by 
members  of  the  class. 

Written  Work 

The  following  table  shows  the  weekly  sales  report  made  by  a 
number  of  salesmen  during  a  certain  week. 

Find  the  total  sales  made  by  each  salesman  during  the  weeki 
and  enter  these  totals  in  the  proper  places  at  the  bottom  of  the 
table. 

Find  the  total  sales  made  each  day,  and  enter  these  totals  in  the 
column  at  the  right. 

Find  the  total  sales  made  by  all  salesmen  during  the  week. 

The  grand  total  should  be  found  in  two  ways:  by  adding  the 
totals  at  the  foot  of  the  blank,  and  those  at  the  right.  If  these 
two  grand  totals  agree,  you  may  assume  that  the  additions  are 
correct ;  if  they  do  not  agree,  you  should  find  the  error. 


DAY 

xI.COLSEK 

D.R.BACOK 

KG.  BATES 

D.O.ESTEY 

TOTAL 

M  ON- DAY 

&/6 

'A5 

^s-^s 

Jf- 

8/C 

9^ 

■3>  /(^ 

^7 

TVESDA Y 

3S-8 

q3 

Cfc7 

8¥- 

yns 

^8 

CH^ 

^7 

-WEDNESDAY 

^/Q. 

s-j 

^c,3 

^7 

<:,3<7 

7/ 

TAS- 

8^ 

THUJiSDAY 

3  SsS- 

/3 

ca^A 

9^ 

yat/- 

// 

•s-cr¥^ 

7^ 

FRIDAY 

^  /  8 

qs. 

'7  /S 

q(. 

(^3q 

3J 

^8¥- 

38 

SATURDAY 

6.3(^ 

4^7 

^3(7 

C& 

7^cr 

^7 

8^C 

<^'A 

TOTAL 

4.  Courtis  Standards.  S.  A.  Courtis  has  determined  certain 
standards  of  achievement  in  addition,  subtraction,  multiplication, 
division,  and  the  copying  of  figures. 

His  test  in  addition  includes  twenty-four  examples  similar  to 
the  two  which  follow. 


ADDITION  9 

127  996 

375  320 

Qrq  778 

^^  *^®  thousands  of  students  examined  by 
means  of  the  Courtis  tests  about  5%  are  able 
to  obtain  the  correct  result  to  twenty-four  such 
examples  in  addition  in  eight  minutes  or  less. 

167  972 

554  119 

Note.  Information  in  regard  to  the  Courtis  Standards  and  Tests  may  be  ob- 
tained by  addressing  S.  A.  Courtis,  Detroit,  Michigan. 

5.  How  to  Rule  a  Blank  Form.  Ruling  the  forms  for  your 
written  work  will  furnish  you  excellent  practice  in  the  use  of  pen, 
ink,  and  ruler.  This  practice  will  be  valuable  as  a  preparation 
for  bookkeeping  in  school  or  in  a  business  office.  Follow  the 
instructions  given  below: 

a.  Make  the  columns  just  wide  enough  for  the  figures,  —  about 
seven  figures  to  an  inch.  Remember  that  the  total  may  have 
one  or  two  more  figures  than  any  of  the  addends  (numbers 
added). 

h.  Make  the  horizontal  lines  parallel  and  about  \  of  an  incn 
apart. 

c.  Make  the  spaces  for  headings  and  totals  f  of  an  inch 
deep. 

d.  Try  to  place  the  form  as  nearly  as  possible  in  the  middle  of 
the  paper. 

6.  How  to  Enter  Statistics.  Much  of  the  clerk's  work  in  a 
business  office  consists  of  entering  statistics  on  ruled  forms. 

a.    Always  write  figures  on  the  line. 
5.    Point  off  figures  in  groups  of  three. 

c.  Make  small  figures;  they  look  better  and  are  more  easily 
read  than  large  ones. 

d.  Keep  the  figures  close  to  the  right  side  of  the  column. 

e.  Keep  the  columns  vertical:  units  above  units,  tens  above 
tens,  etc. 

/.    Write  the  figures  at  equal  distances  from  each  other. 


10 


ADDITION 


Written  Work 

1.  The  following  table  shows  the  delivery  records  of  a  store 
running  five  wagons.  A  record  of  each  day's  deliveries  is  kept 
and  the  week's  totals  are  found.  If  the  summary  shows  that  any 
one  wagon  is  required  to  make  an  unreasonably  large  number  of 
deliveries,  a  change  in  the  routes  may  be  necessary.  By  finding 
the  total  number  of  deliveries  made  each  week,  the  average  cost 
per  delivery  may  be  computed. 


X>AY- 

■VfAGOK 

WAOOJV 
HO  2. 

JV0  3 

■iYAOOK 
J^OJ/- 

TOTAL 

MOKDAY 

:i^3 

<!>/Cf 

3.7  S 

/  /A5> 

S.Uf 

TUrSVAY 

Ji./C 

3^^ 

3cf/ 

/nfZ 

wrourSDAY 

£.sy 

ZS'T 

2.^^ 

/Zf 

33,2. 

TKUJZSDAY 

30/ 

Z,Cf/ 

3^/ 

/^^-r 

Cb^C> 

mi  DAY 

Ht?^ 

3x0  U 

3nS> 

3./E 

3./^ 

SATVJiDAY 

3/8 

3^/ 

^a.o 

ibii,3 

^o/ 

TOTAL 

G-X. 

Rule  a  blank  form  similar  to  this  model;  copy  the  statistics, 
and  find; 

a.  The  total  number  of  deliveries  made  during  the  week  by 
each  wagon. 

h.    The  total  number  of  deliveries  made  each  day. 
c.    The  total  numbel*  of  deliveries  for  the  week. 

2.  Rule  a  blank  form  similar  to  the  first  of  the  tables  on  the 
opposite  page,  copy  the  statistics,  and  find  the  totals  indicated. 

3.  Referring  to  the  second  of  the  tables  on  the  opposite  page, 
what  was  the  value  of  each  crop  in  each  of  the  geographical  divi- 
sions, and  in  the  entire  United  States  ? 

Rule  a  blank  in  ink  and  indicate  these  values  as  totals. 


ADDITION 


11 


Weekly 

Sales  Report  by  Departments 

Dept. 
No. 

Monday 

TXXESDAT 

"Wednesday 

Thursday 

Friday 

Saturday 

Total 

1 

$932.87 

$823.75 

$239.75 

$724.16 

$295.16 

$840.19 

2 

829.47 

584.92 

395.58 

645.97 

396.74 

492.10 

3 

723.85 

486.47 

523.78 

419.52 

296.15 

492.58 

4 

836.47 

594.38 

723.91 

391.16 

749.15 

581.07 

6 

486.74 

432.95 

312.85 

492.43 

723.85 

239.57 

6 

728.74 

483.96 

472.58 

439.17 

396.14 

211.64 

7 

385.75 

539.59 

542.87 

734.67 

723.96 

447.92 

8 

648.57 

823.85 

514.29 

439.76 

824.57 

238.11 

9 

923.37 

239.73 

629.85 

329.54 

385.47 

294.10 

10 

473.48 

865.94 

518.59 

172.39 

749.80 

663.19 

Total 

Grand  Total 

Value  of  the  Wheat,  Corn,  and  Oat  Crops  in  the  Various  States 
(In  Thousands  of  Dollars) 


State  and  Division 

Corn 

Wheat 

Oats 

State  and  Division 

Corn 

Wheat 

Oats 

Maine        ... 

480 

72 

2,347 

Minnesota     .     .     . 

28,925 

48,938 

31,962 

New  Hampshire 

794 

225 

Iowa     .     .     . 

151,207 

10,023 

58,811 

Vermont    .... 

1,296 

24 

1,589 

Missouri   .     ,      . 

112,196 

21,375 

12,994 

Massachusetts    .     . 

1,629 

128 

North  Dakota 

3,766 

99,236 

20,948 

Rhode  Island      .     . 

401 

26 

South  Dakota 

28,248 

36,008 

13,098 

Connecticut   .     .     . 

2,310 

166 

Nebraska  .     . 

67,568 

37,985 

.16,653 

New  York      .     .     . 

13,834 

7,054 

38,797 

5,306 

1,433 

21,204 

15,420 

814 

14,915 

Kansas      .     . 
N.  C.  W.  Miss 

Kentucky 
Tennessee 
Alabama   .     . 

R. 

69,690 

68.295 

19,264 

New  Jersey    .     .     . 
Pennsylvania      .     . 

60,192 
53,862 
42,802 

6.791 

7,077 

359 

N.  Atlantic     .     . 

1,775 
2,632 
3,224 

Mississippi     . 

40,356 

93 

1,180 

Louisiana  .     . 

22,093 

361 

Delaware        .     .     . 

3,381 

1,864 

55 

Texas    .     .     . 

98,112 

10.253 

13,390 

Maryland       .     .     . 

13,450 

8,536 

608 

Oklahoma 

41,770 

15,072 

7,988 

Virginia     .... 
West  Virginia     .     . 

33,739 
15,928 

8,682 
3,412 

2,020 
1,461 

Arkansas   .     . 

33,828 

884 

1,741 

S.  Central 
Montana  .     . 

N   Carolina 

42,418 
29,136 

5,907 
865 

2,352 
4,598 

S.  Carolina     ,     .     . 

428 

12.381 

7.997 

Georgia      .... 

45,864 

1,498 

4,921 

Wyoming  .     . 

236 

1.745 

3,171 

Florida       .     . 

6,727 

518 

Colorado    .     . 
New  Mexico 
Arizona     .     . 

4,368 

1,562 

528 

8,006 
1,109 

778 

4,717 

S.  Atlantic      .     . 

828 

188 

Utah     .     .     . 

202 

4,544 

2,069 

Nevada      .     . 

29 

1,137 

208 

Ohio 

78,484 

9,565 

30,782 

Idaho    .     .     . 

276 

9,613 

5,956 

Indiana      .... 

83,733 

9,374 

23,940 

Washington   . 

651 

36,535 

5,476 

Illinois       .... 

174,791 

8.641 

54,818 

Oregon       .     . 

472 

15,132 

5,623 

Michigan  .... 

31,492 
29,714 

6,720 
2,958 

17,103 
27,119 

California 
Far  Western 

1,635 

5,850 

4,290 

Wisconsin       .     .     . 

N.  C.  E.  Miss.  R. 

United  Stat 

es  . 

Note.    Different  classes,  or  different  groups  of  students  of  the  same  class,  should  be  held  responsible 
for  computing  the  desired  sums  for  different  geographical  divisions. 


12  ADDITION 


Checking  Addition  by  Casting  Out  Nines 

7.  Excess  of  Nines.  The  remainder  after  dividing  any  number 
by  nine  is  called  the  Excess  of  Nines.  If  the  number  47  is 
divided  by  9,  the  excess  of  nines  is  2.  The  excess  of  nines  in  30 
is  3,  because  when  30  is  divided  by  9,  there  is  a  remainder  of  3. 
When  we  "  cast  out  nines  "  from  a  number,  we  divide  the  number 
by  9,  and  indicate  the  excess. 

What  is  the  excess  of  nines  in  17  ?    14  ?    39  ?    45  ?    117  ?    23  ? 

8.  Method  of  Checking.  If  two  numbers,  each  exactly  divis- 
ible by  9,  are  added,  their  sum  also  is  divisible  by  9.  If  one 
number  with  an  excess  of  3  is  added  to  a  number  with  an  excess 
of  2,  the  sum  will  have  an  excess  of  5.  The  excess  of  nines  in  a 
sum  is  equal  to  the  excess  in  the  sum  of  the  excesses  of  the  numbers 
added. 

Examples.  Add  80  and  19;  check  the  result  by  casting  out 
nines. 

Solution  :    30  +  19  =  49. 

The  excess  of  nines  in  the  sum,  49,  is  4. 
30  has  an  excess  of  3 ; 
19  has  an  excess  of  1. 

The  sum  of  the  excesses  of  the  numbers  added  is  4,  therefore  the 
addition  checks. 

For  convenience,  the  work  may  be  arranged  as  follows : 

Numbers  Added    Excesses 


a.            30 

3 

19 
Sura  49 

1 
4 

Excess  of  sum   4 

NuMBBBS  Added    Excesses 

NiTMBBBS  Added 

EXOESBBS 

h.           23            5 

c.           49 

4 

13            4 

34 

7 

Sum  36            9  or  0 

Sum  83 

11  or  2 

Excess  of  sum  0 

Excess  of  sum   2 

CASTING  OUT  NINES  13 

9.  Short  Method  of  Finding  the  Excess.  The  excess  of  nines  in 
any  number  may  be  found  by  the  following  method  : 

Add  the  digits  composing  the  number.  If  the  sum  is  composed  of 
two  or  more  digits  add  them.  Continue  this  procedure  until  a  result  of 
one  digit  is  secured. 

Examples.     1.    What  is  the  excess  of  nines  in  25  ? 

Solution  :  2  +  5  =  7,  the  excess. 

2.    What  is  the  excess  of  nines  in  328  ? 

Solution:  3  +  2  +  8  =  13 

1  +  3  =  4,  the  excess. 

The  addition  of  digits  to  find  the  excess  will  be  further  sim- 
plified by  observing  the  following  suggestions  : 

a.  Ignore  9's,  and  combinations  which  add  to  9  or  multiples 
of  9. 

Example.     What  is  the  excess  of  nines  in  9457  ? 

Solution  :  Ignore  9  and  5  +  4 ;  the  excess  is  7. 

h.  When  the  addition  results  in  a  number  of  two  digits,  add 
the  digits  and  proceed  as  before. 

Example.     What  is  the  excess  of  nines  in  7528  ? 

Solution  :  7  +  5  =  12;l  +  2  =  3; 

3  +  2  +  8  =  13;     1  +  3  =  4,  the  excess. 

10.  Limitation  of  the  Method.  Casting  out  nines  is  not  an  abso- 
lute check  for  any  process.  It  will  not  disclose  an  error  of  9  or 
any  multiple  of  nine,  neither  will  it  disclose  an  interchange  of 
digits,  such  as  763  for  673. 


14 


ADDITION 


Add  and  check 


Written  Work 


Numbers  to  bk 
Added 

EXCESSKS 

213 

412 
617 
362 
145 
215 
829 
657 
923 

? 

9 
? 
? 
? 
? 
? 

? 
? 

? 

? 

2.  Rule  a  suitable  blank  form  for  the  following  :  At  the  right 
of  each  column  of  figures  rule  a  narrow  column  in  which  to  indi- 
cate the  excesses. 

Find  the  totals  as  indicated  ;  check  all  additions  by  casting 
out  nines. 

Value  of  Farm  Lands,  Buildings,  and  Implements  in  the 
United  States 


Division 

Land 

Ex. 

Buildings 

Ex. 

Implements 

Ex. 

Total 

Ex. 

New  England   . 
Middle  Atlantic 
E.N.  Central    . 
W.N.  Central  . 
South  Atlantic  . 
E.  S.  Central     . 
W.S.  Central    . 
Mountain .    .    . 
Pacific.    .    .    . 

382,134,424 
1,462,321,005 
7,231,699,114 
10,052,560,913 
1,883,349,675 
1,326,826,864 
2,716,098,530 
1,174,370,096 
2,246,313,548 

336,410,384 
980,628,098 
1,642,292,480 
1,562,104,957 
603,086,799 
411,570,975 
412,498,352 
145.026,777 
231,832,706 

50,798,826 

167,480,384 

268,806,550 

368,635,544 

98,230,147 

75,339,333 

119,720,377 

49,429,975 

66,408,647 

U.S.  Totals  . 

Grand  Total 

3.  The  following  table  shows  a  method  used  by  department 
stores  to  determine  the  cost  of  the  purchases  made  for  various 
departments  during  the  month.     For  example,   Invoice   No.    1, 


CASTING  OUT  NINES 


15 


purchased  on  January  2,  included  goods  for  the  six  departments 
of  the  store.  Invoice  No.  2  included  goods  for  only  three  depart- 
ments. 

The  total  amount  of  the  invoice  may  be  found  by  horizontal 
addition. 

The  total  purchases  for  each  department  during  the  month  may 
be  found  by  vertical  addition. 

Rule  a  blank  suitable  for  this  material,  enter  the  data,  and  find: 

a.    The  total  of  each  invoice. 

h.    The  total  purchases  for  each  department  during  the  month. 

c.    The  total  purchases  for  all  departments  during  the  month. 

Check  all  additions  by  casting  out  nines. 


Invoice  No. 

Date 

Deft.  1 

Dept.2 

Dept.  3 

Dept.  4 

Dept.  5 

Dept.  6 

Total 

1 

Jan. 

2 

129 

30 

340 

60 

290 

39 

360 

89 

240 

30 

376 

80 

2 

Jan. 

3 

276 

90 

347 

80 

174 

44 

3 

Jan. 

3 

295 

67 

298 

87 

350 

27 

289 

67 

287 

57 

4 

Jan. 

o 

246 

32 

238 

47 

350 

27 

347 

25 

250 

68 

276 

57 

5 

Jan. 

6 

231 

53 

350 

21 

378 

89 

190 

23 

6 

Jan. 

8 

212 

23 

325 

67 

345 

67 

367 

78 

310 

57 

185 

67 

7 

Jan. 

8 

227 

85 

346 

78 

357 

89 

298 

67 

8 

Jan. 

10 

170 

67 

9 

Jan. 

11 

160 

87 

325 

67 

287 

67 

367 

57 

287 

00 

189 

00 

10 

Jan. 

15 

170 

97 

341 

28 

321 

67 

378 

98 

287 

89 

11 

Jan. 

15 

180 

89 

333 

33 

278 

90 

2.34 

86 

12 

Jan. 

15 

345 

67 

345 

67 

328 

98 

300 

00 

350 

90 

13 

Jan. 

16 

203 

25 

356 

78 

378 

68 

14 

Jan. 

17 

204 

67 

367 

78 

376 

56 

267 

87 

347 

52 

15 

Jan. 

19 

290 

87 

356 

87 

278 

65 

378 

67 

16 

Jan. 

23 

297 

76 

347 

89 

398 

67 

256 

28 

250 

00 

17 

Jan. 

24 

234 

56 

388 

88 

18 

Jan. 

25 

245 

67 

287 

98 

367 

34 

256 

78 

234 

56 

19 

Jan. 

28 

229 

39 

323 

23 

376 

29 

234 

56 

167 

89 

20 

Jan. 

31 

236 

78 

310 

21 

289 

98 

387 

85 

245 

67 

245 

67 

■ 

Total 

CHAPTER  II 
SUBTRACTION 

11.  Drill  Tables.  Daily  practice  on  the  following  combinations 
will  increase  your  speed  and  accuracy  in  the  process  of  subtraction. 

Drill  on  these  combinations  until  you  can  state  all  of  the  results 
in  less  than  thirty  seconds. 

9879674736878458 
2153124436438213 


2 

7 

9 

5 

9 

5 

6 

5 

9 

4 

4 

9 

8 

2 

6 

8 

1 

7 

4 

5 

5 

4 

3 

2 

7 

4 

3 

8 

5 

2 

4 

6 

5 

8 

4 

8 

6 

7 

7 

9 

8 

1 

3 

3 

5 

7 

9 

6 

3 

8 

1 

6 

2 

1 

6 

1 

2 

1 

2 

1 

5 

7 

6 

5 

Drill  on  the  following  until  you  can  state  all  of  the  results  in 
less  than  thirty  seconds. 

16      14      15      18      13      17      12      11      16      11      12      17      11 

8689495976684 


13      12      15      16      11      12      12      12      11      13      15     11      12 

5369        3        38779789 


11 

12 

13 

14 

14 

13 

14 

15 

14 

11 

13 

5 

4 

7 

8 

7 

6 

5 
16 

9 

9 

2 

8 

SUBTRACTION 


17 


When   performing   subtraction,  one   is   frequently   obliged   to 
"borrow"  as  in  the  following. 

Copy  these  examples,  and  make  the  subtractions. 


1. 

479 

284 

2. 

636 
198 

3. 

4279 

3682 

4. 

14973 

8297 

5. 

3084 
1596 

6. 

12379 
3084 

7. 

42937 
39048 

8. 

946320 

298452 

9. 

37649 

20863 

10. 

947302 
842943 

11. 

794680 
409694 

12.    Checking   Subtraction.     Subtraction   may    be    checked   by 
either  of  the  following  methods : 

(a)  Difference  +  Subtrahend  =  Minuend. 
(6)  Minuend  —  Difference  =  Subtrahend. 


Example. 

Solution.    78   Minuend 

21_  Subtrahend 
57  Diiference 


Subtract  21  from  78 
Check. 


a.   57   Difference 
21    Subtrahend 
78    Minuend 


b,   78  Minuend 
57  Difference 
21   Subtrahend 


Written  Work 

Perform  the  subtractions   indicated ;    check  the  first  five  by 
method  (a),  and  the  last  five  by  method  (5), 


1. 

2. 

3. 

4. 

5. 

489 

7932 

82578 

63217 

49216 

392 

494 

58214 

41283 

21953 

6. 

7. 

8. 

9. 

10. 

68310 

40513 

53821 

79608 

184732 

49168 

39458 

41927 

20973 

75806 

11.  The  following  data  show  the  sales  in  the  various  depart- 
ments of  a  large  store  for  the  month  of  August,  1914,  and  the 
month  of  August,  1915. 


18 


SUBTRACTION 


Rule  a  blank  similar  to  the  following: 

Comparative   Sales   Record 


Depart- 
ment No. 

August,  1914 

August,  1915 

Increase  o* 
Decrease 

1 

$  5,483.85 

$  5,834.75 

2 

7,239.74 

8,238.74 

3 

15,493.67 

14,835.92 

4 

9,834.56 

10,385.47 

5 

23,842.12 

22,147.94 

6 

15,858.43 

16,614.34 

7 

6,395.75 

6,114.32 

8 

19,432.86 

22,324.73 

9 

9,445.87 

10,302.95 

10 

43,221.42 

46,932.56 

11 

29,496.56 

31,416.47 

12 

18,853.16 

17,542.85 

13 

22,542.19 

25,436.83 

14 

25,746.91 

24,427.85 

15 

18,422.16 

21,541.86 

Total 

Enter  the  sales  in  the  proper  column  of  the  blank. 

Find  the  increase  or  decrease  in  the  amount  of  the  sales  in 
each  department  for  August,  1915,  over  the  sales  in  the  same  de- 
partment for  August,  1914. 

Enter  increases  in  black  ink;  decreases  in  red  ink. 

Find  the  net  increase  for  the  entire  store. 

12.  The  following  shows  the  total  population  of  the  United 
States  for  the  years  indicated. 

1790  —  3,929,214;       1800—  5,308,483 

1830—12,866,020 

1860—31,443,321 

1890  —  62,947,714 


1810—  7,239,881 
1840—17,069,453 
1870—38,558,371 
1900—75,994,575 


1820—9,638,453; 

1850—23,191,876; 

1880—50,155,783; 

1910  —  91,972,266. 

Rule  a  blank  form  to  show  the  year  the  census  was  taken,  the 
population  each  census  year,  and  the  increase  in  population  for 
each  interval  of  10  years. 

See  how  simple  you  can  make  this  blank. 


SUBTRACTION 


19 


13.    Rule  a  form,  enter  the  following  statistics,  find  the  gross 
profit  of  each  department,  and  the  gross  profit  of  the  entire  store. 

Gross  Profit  of  a  Department  Store 


Dept.  No. 

Sales 

Cost  of  Goods 
Sold 

Gkoss  Profit 

1 

$5,629.80 

$4,984.37 

2 

7,358.92 

6,295.16 

3 

4,916.09 

4,192.86 

4 

7,329.16 

6,593.54 

5 

10,609.15 

9,835.17 

6 

6,123.18 

5,902.52 

7 

7,212.47 

6,275.43 

8 

9,475.37 

8,594.48 

9 

4,238.16 

3,725.91 

10 

5,824.78 

5,014.78 

Total 

14.    Rule  a  suitable  form,  enter  the  following  statistics,  and  find  : 

a.    The  gross  profit  by  departments. 

h.    The  gross  profit  of  the  entire  store  (two  ways). 

c.  The  net  profit  or  net  loss  by  departments;  enter  net  profit  in 
black,  net  loss  in  red. 

d.  Net  profit  or  net  loss  of  the  entire  store  (two  ways). 


Dept.  No. 

Sales 

Cost  of 
Goods  Sold 

Gross  Profit 

Expenses 

Net  Profit 
OR  Loss 

1 

$7816.40 

$6715.32 

$423.85 

2 

9317.42 

849^.17 

530.08 

3 

6842.56 

5914.72 

731.96 

4 

7319.62 

6593.57 

671.42 

5 

8295.17 

7942.17 

456.72 

6 

5732.88 

5101.59 

322.75 

7 

9514.82 

8899.55 

693.15 

8 

2289.74 

1856.80 

216.77 

9 

5793.66 

5135.60 

788.51 

10 

9559.38 

8625.50 

523.80 

13.  Subtracting  by  Adding  Complements.  A  series  of  additions 
and  subtractions  may  be  performed  by  the  method  of  adding  com- 
plements. 


20  SUBTRACTION 

The  difference  between  any  number  and  the  next  higher  power 
of  10  is  called  the  complement  of  the  number.  Thus,  the  comple- 
ment of  7  is  3  ;  the  complement  of  6  is  4  ;  the  complement  of  83 
is  17. 

If,  instead  of  subtracting  a  number  less  than  ten  from  a  given 
number,  its  complement  be  added,  the  result  will  be  10  too  large. 
Thus,  13  -  6  =  7  or  13  +  4  =  17  (a  result  10  too  large). 

If,  instead  of  subtracting  two  numbers  less  than  ten  from  a 
given  number,  their  complements  are  added,  the  result  will  be  20 
too  large  ;  if  the  complements  of  three  such  numbers  are  added, 
the  result  will  be  30  too  large,  etc. 

Examples.     1.    29-6-7  =  ? 

Solution.  29  +  4  +  3  =  36.  Since  two  complements  were  added,  the  re- 
sult is  20  too  large.     Therefore,  subtract  20,  leaving  16. 

2.  38-4-7-8  =  ? 

Solution.  38  +  6  +  3  +  2  =  49.  Since  three  complements  were  added,  sub- 
tract 30,  leaving  19. 

3.  46-8  +  4-7=? 

Solution.  46  +  2  +  4  +  3  =  55.  Since  two  complements  were  added,  20 
must  be  subtracted,  leaving  35. 

The  practical  value  of  this  method  will  be  shown  by  solving  the 
following  examples. 

1.    36-24  +  19-12+21-13-6=? 

Solution.  By  combining  as  indicated  in  the  units'  column,  beginning 
36      at  the  top  (complements  are  marked  with  an  *)  we  have 

—  24  6  +  6*  +9  +  8*  +1  +  7*  +  4*  =  41 

^^  Since  four  complements  were  added,  the  result  is  40  too  large. 

—  12      Therefore  write  1  and  drop  the  4. 

21 

^  o  By  combining  as  indicated  in  the  tens'  column  we  have 

_    g  3  +  8*  + 1  + 9* +2 +  9*  =  32 

•  21  Since  three  complements  were  added,  the  result  is  30  too  large. 

Write  2  and  drop  the  3. 

Result,  21. 


SUBTRACTION  21 

2.    985  +  234-126-34-125-174  +  386=? 

985 

234         Solution.  Combining  in  the  units'  column,  beginning  at  the  top 

—  126     "^'^  have 

_     3^  5  +  4  +  4*  +  6*  +  5*  +  6*  +  6  =  36 

1  oc 

tt^A         Write  the  6.     Since  four  complements  were  added,  the  result  is  40 

"  ooa     ^^  large.     Therefore  we  must  drop  the  3  in  36,  and  also  subtract  1 
from  the  8  at  the  top  of  the  tens'  column. 
1146 

Combining  in  the  tens'  column  we  have 

7  +  3  +  8*  +  7*  +  8*  +  3*  +  8  =  44 

Since  four  complements  were  added,  we  must  deduct  40,  leaving  4  which  is 
written  in  the  tens'  column  of  the  result. 

Combining  in  the  hundreds'  column  we  have 

9  +  2  +  9*  +  9*  +  9*  +  3  =  41 

Three  complements  were  added,  the  result  is  therefore  30  too  large.     Sub- 
tract 30  and  write  11. 

Result,  1146. 

Oral  Work 
Find  the  results  by  the  addition  of  complements  : 


1. 

46  -  4  -  7  = 

2. 

72-8-6-3  = 

3. 

39_7  +  3-9  = 

. 

4, 

48-17-6  = 

5. 

81  _  23  -  42  = 

6. 

49  -  22  +  15  -  11 

7. 

85-26-35  +  62- 

16  = 

8. 

643  -  289  +  364  = 

9. 

781  _  247  +  64  = 

10. 

1046-987+649  = 

11. 

943  -  876  +  629  = 

12. 

1349  -  268  +  421  = 

13. 

1264  -  34  +  1321  = 

14. 

1789  -  347  +  736  = 

15. 

16. 

17. 

2346 

1932 

923,578 

+  1267 

+  9845 

-  5,284 

~  321 

-  932 

+  28,956 

+  6964 

+  2122 

- 123,749 

-1235 

-2375 

+  83,219 

+  367 

-   23 

-  259,734 

-2960 

+  692 

+ 125,982 

-  985 

-1243 

-  429,764 

22 


SUBTRACTION 


Written  Work 

1.  The  following  model  shows  the  ruling  of  the  ledger  in  which 
banks  keep  accounts  with  their  depositors.  Deposits  are  added 
to  the  balance  of  the  previous  day,  and  checks  are  subtracted, 
to  find  the  new  balance  to  the  credit  of  the  depositor's  account. 

Find  the  daily  balances: 

William  Hatfield 


Date 

Deposits 

Checks 

Balance 

June  1 

$328.57 

$  85.68 

$   14.25 

? 

2 

125.80 

65.90 

12.73 

? 

3 

245.85 

127.89 
114.56 

35.87 

? 

4 

319.45 

38.51 

26.82 

102.50 

? 

5 

95.90 
141.66 

95.68 

? 

6 

450.00 

132.88 

6.20 

? 

8 

139.75 

216.45 
39.46 
19.99 

213.55 

66.82 

? 

2.    The  following  blank  shows  a  convenient  method  of  keeping 
a  record  of  cash  received  and  paid  by  a  small  business. 
Rule  a  blank  similar  to  the  model  and  enter  the  statistics. 


Date 

Cash  Kboeived 

Cash  Paid 

Daily  Cash 

Cash  Sales 

On  Account 

Purchases 

On  Account 

Expenses 

Balance 

Feb.  1 

1 

2 

$215.78 
294.80 

$124.35 

95.88 

$  80.75 
157.47 

$  68.55 
113.25 

$  8.75 
3.73 

$216.27 
? 
? 

3 

188.47 

148.23 

95.48 

316.57 

27.49 

? 

4 

218.43 

49.47 

17.49 

42.39 

9.12 

? 

5 

388.92 

112.67 

221.81 

76.29 

75.84 

? 

6 

478.07 

290.04 

88.12 

448.14 

6.90 

? 

? 

? 

? 

? 

? 

? 

SUBTRACTION  23 

a.    Find  the  daily  cash  balances. 

To  the  balance  of  the  preceding  day  add  the  receipts  from  cash 
sales  and  receipts  on  account,  and  subtract  the  various  amounts 
listed  under  "  Cash  Paid." 

Thus,  1216.27  -f  215.78  +  124.35  -  80.75  -  68.55  -  8.75  =  ? 

h.    Find  the  totals  for  each  column. 

3.    Add  upward;  subtract  across: 

a.    7,463-2,847=  5.    174,638-94,273  = 

5,928-3,804=  38,270-27,409  = 

9,604-2,870=  70,563-  2,879  = 

3,962  -  1,436  =  924,360  -  14,287  = 

9,287-5,426=  7,503-  2,769  = 


CHAPTER   III 


MULTIPLICATION 


Accuracy  and  speed  in  multiplication  depend  largely  upon  a 
thorough  mastery  of  the  multiplication  tables.  The  student  should 
thoroughly  review  the  tables  previously  learned  and  should  con- 
tinue with  daily  drills  on  combinations  up  to  25  times  25. 


14.   Drill  Tables. 

Multiply  across  ;  add  upward  : 

1. 

2. 

3. 

4. 

74  X  436  = 

83  X  423  = 

25  X  624  = 

35  X  624  = 

74  X  523  = 

83x157  = 

25  X  726  = 

35  X  706  = 

74  X  287  = 

83  x  284  = 

25  X    37  = 

35  X  753  = 

74  X  492  = 

83  X  307  = 
83  X  596  = 

25  X  869  = 
25  X  493  = 

35  X  496  = 

74  X    ?    = 

35  X  548  = 

83  X    ?    = 

25  X  468  = 

35x784  = 

25x    ?    = 

35  X    ?    = 

Oral  Work 

Use  2,  3,  4,  5, 

6,  7,  8,  and  9  as 

multipliers. 

Name  the  results 

V  each  column 

in  less  than  20  seconds. 

1. 

2.                      3. 

4. 

5. 

3 

18                  5 

4 

9 

5 

10                  8 

9 

11 

7 

4                12 

15 

16 

14 

7                15 

20 

30 

11 

9                  7 

17 

25 

6 

15                30 

8 

14 

8 

16                22 

13 

17 

9 

20                16 

18 

11 

15 

12                25 

22 

16 

24 


MULTIPLICATION 


25 


Written  Work 

1.    A  factory  made  an  investigation  of  the  number  of  articles  of 

a  certain  kind  manufactured  by  each  of  its  employees.     It  found 

that ; 

9  men  produced  46  articles  each. 

9  men  produced  48  articles  eacli. 

11  men  produced  53  articles  each. 
15  men  produced  55  articles  each. 
18  men  produced  59  articles  each. 
23  men  produced  61  articles  each. 
25  men  produced  62  articles  each. 
25  men  produced  63  articles  each. 
21  men  produced  64  articles  each. 
17  men  produced  63  articles  each. 
17  men  produced  6Q  articles  each. 
14  men  produced  68  articles  each. 

12  men  produced  69  articles  each. 
8  men  produced  70  articles  each. 

Rule  a  form  with  a  heading  similar  to  the  following  : 
Production   Record 


NuMBlEE  OF  Men 


Number  of  Articles 
Made  by  Each 


Total 


Enter  the  statistics,  find  the  number  of  articles  produced  by 
each  group  of  employees,  and  the  total  number  of  articles  produced 
by  all  of  the  employees. 

2.  Nine  workmen  were  employed  in  the  manufacture  of  differ- 
ent articles,  and  were  paid  a  certain  number  of  cents  for  each 
piece  completed.  Complete  the  following  table,  finding  the 
wages  earned  by  each  workman. 


26 


MULTIPLICATION 


Daily  Piecework  Labor   Cost 


Workman 

No. 

Number  of 
Articles  Made 

WAr.E  Kate 
PER  Piece 

Wages  Earned 

1 

17 

$0.27 

2 

19 

.22 

3 

38 

.16 

4 

79 

.06 

5 

32 

.15 

6 

28 

.18 

7 

64 

.07 

8 

81 

.05 

9 

29 

.21 

15.  Checking  Multiplication.  Multiplication  may  be  checked 
by  several  methods.     The  following  methods  are  commonly  used. 

a.  Repeating  the  multiplication  and  assuming  that  if  the  same 
product  is  obtained  the  work  is  correct.  This  is  not  a  reliable 
check  because  an  error  may  be  repeated. 

h.  Dividing  the  product  by  the  multiplier  to  obtain  the  multi- 
plicand, or  by  the  multiplicand  to  obtain  the  multiplier. 

c.    Casting  out  nines. 

16.  Casting  Out  Nines.  The  method  is  as  follows  :  Find  the 
excess  of  7iines  in  the  multiplicand  and  in  the  multiplier.  Find  the 
product  of  these  excesses.  Find  the  excess  of  nines  in  this  product. 
It  should  equal  the  excess  of  nines  in  the  result. 

Example.     Multiply  23  by  16  ;  check  by  casting  out  nines. 

Solution.   23      5  =  the  excess  of  nines  in  23. 
16       7  =  the  excess  of  nines  in  16. 
368     35  =  the  product  of  these  excesses. 
Check.  8  =  the  excess  in  this  product. 

The  excess  of  nines  in  368  is  also  8.     The  multiplication,  therefore,  checks. 

Without  performing  the  multiplications  determine  the  probable 
correctness  of  the  following  products,  by  means  of  casting  out  nines : 


1. 

25 

38 
950 


2. 

82 
35 


3. 

36 

87 


4. 

286 
37 


5. 

4172 
39 


6. 

344 

281 


7. 

733 
492 


2870       3132       10,382       162,698       96,664       362,636 


MULTIPLICATION 


27 


8. 

398 
241 


9. 

43,962 
47,835 


95,918 


2,102,922,270 


10. 

34,276 
21,578 


738,627,528 


Written  Work 
Multiply  and  check  by  casting  out  nines  : 
11.  12.  13.  14.  15.  16. 

347  279  627  132,879  63,154  78,293,567 

861  439  123  642,378  9,837  20,417,839 


17.    The  following  table  gives  information  regarding  the  corn 
crop  in  the  United  States  in  a  recent  year. 

Corn  Production  in  the  United  States 


States 


North  Atlantic 

Maine 

New  Hampshire 

Vermont 

Massachusetts 

Rhode  Island 

Connecticut 

New  York 

New  Jersey 

Pennsylvania 

South  Atlantic 

Delaware 

Maryland    ....... 

Virginia 

West  Virginia 

North  Carolina 

South  Carolina 

Georgia 

Florida 

North  Central,  East  of  Miss. 

Ohio 

Indiana 

Illinois 

Michigan 

Wisconsin 


Number  of 

Thousands  of 

Acres 


16 

23 

45 

47 

11 

60 

512 

273 

1,499 


195 

670 
1,980 

725 
2,808 
1,915 
3,910 

655 


4,075 
4,947 
10,658 
1,625 
1,632 


Average  Yield 
PER  Acre 


40.0 
46.0 
40.0 
45.0 
41.5 
50.0 
38.6 
38.0 
42.5 


34.0 
36.5 
24.0 
33.8 
18.2 
17.9 
13.8 
13.0 


42.8 
40.3 
40.0 
34.0 
35.7 


Average  Price 

PER  Bushel. 

IN  Cents 


75 
75 
75 

77 
86 
77 
70 
68 
63 


51 
55 
71 
65 

83 
85 
85 
79 


45 
42 
41 
57 
51 


28 


MULTIPLICATION 


Corn  Production  in  the  United  States  —  Continued 


States 


Number  of 

Thousands  of 

Acres 


Average  Yield 
PER  Acre 


North  Central,  West  of  Miss. 

Minnesota 

Iowa 

Missouri 

North  Dakota 

South  Dakota 

Nebraska 

Kansas 

South  Central 
Kentucky    .     .     .     ....     . 

Tennessee 

Alabama 

Mississippi 

Louisiana 

Texas      

Oklahoma 

Arkansas     

Far  Western 
Montana     ........ 

Wyoming 

Colorado 

New  Mexico 

Arizona 

Utah  . 

Nevada  

Idaho      

Washington 

Oregon 

California 


2,266 
10,047 
7,622 
328 
2,495 
7,609 
7,575 


3,600 
3,332 
3,150 
3,106 
1,805 
7,300 
5,448 
2,475 


24 

16 

420 

93 

19 

9 

1 

12 

31 

20 

52 


34.5 
43.0 
32.0 
26.7 
30.6 
24.0 
23.0 


30.4 
26.5 
17.2 
18.3 
18.0 
21.0 
18.7 
20.4 


25.5 
23.0 
20.8 
22.4 
33.0 
30.0 
30.0 
32.8 
27.3 
31.5 
37.0 


Prepare  a  blank  similar  to  the  modeL 


States 

Acres 

Average 

Yield  per 

Acre 

Total 
Bushels 
Produced 

Average 

Price  per 

Bushel 

Total 
Crop  Value 

Ex. 

Ex. 

Ex. 

Ex. 

$ 

i 

Ex. 

SHORT  METHODS  20 

a.  Find  the  total  number  of  bushels  of  corn  produced  in  each 
state. 

h.    Find  the  total  value  of  the  corn  crop  of  each  state. 

Different  classes  or  various  groups  of  a  class  should  make  the  required  com- 
putations for  assigned  geographical  divisions  of  the  country.  In  checking  the 
results,  the  "excesses"  should  be  placed  in  the  columns  marked  "Ex." 

Many  interesting  comparisons  may  be  made  from  the  data  of  the  preceding 
table.  For  illustration :  Name  the  five  states  which  produced  the  most  corn 
and  compare  the  yields  in  these  states.  What  geographical  section  of  the 
country  produced  the  largest  corn  crop?  What  relation,  if  any,  is  there 
between  the  size  of  the  corn  crop  in  the  various  states  and  the  average  price 
per  bushel  in  the  various  states  ? 

Short  Methods  op  Multiplication 

These  short  methods  will  be  found  to  be  very  practical.  Master 
two  or  three  of  them  thoroughly  before  taking  up  others.  Use 
those  that  you  have  mastered  whenever  you  have  opportunity  to 
do  so.  It  is  not  necessary  that  all  of  these  short  methods  be 
mastered  before  the  succeeding  chapters  are  studied. 

17.    To  multiply  by  10,  100,  1000,  10000,  etc. 

a.  When  the  multiplicand  is  an  integer.  Annex  to  the  multi- 
plicand as  many  zeros  as  there  are  zeros  in  the  multiplier. 

Thus,  to  multiply  an  integer  by  10,  annex  one  zero ;  to  multiply 
by  100,  annex  two  zeros. 

Examples.     1.  37  x  10  =  370.       2.   29  x  100  =  2900. 

h.  When  the  multiplicand  is  a  decimal  fraction.  Move  the 
decimal  point  as  many  places  to  the  right  as  there  are  zeros  in  the 
multiplier. 

It  may  be  necessary  to  annex  zeros  in  order  to  move  the 
decimal  point  the  desired  number  of  places. 

Examples.     1.    Multiply  .1357  by  100. 

Solution.    Move  the  decimal  point  two  places  to  the  right,  13.57- 

2.    Multiply  32.46  by  1000. 

Solution.  In  order  to  move  the  decimal  point  three  places  to  the  rightr  it 
is  necessary  to  annex  one  zero,  giving,  as  a  result,  32,460. 


30 


MULTIPLICATION 


Oral  Work 

Multiply  as  indicated  : 

1.    37,946x100. 

2. 

5293  X  10,000. 

3.    639x100,000. 

4. 

120  X  1000. 

5.    .376x1000. 

6? 

1.349  X  1000. 

7.    27.9637x100. 

8. 

.000932  - 10. 

9.    .00873x1000. 

10. 

.7032  X  1000. 

11.    3.69  x  1000. 

12. 

.0027  X  100,000. 

13.    1427.834x10,000. 

14. 

625.086  X  1000. 

18.    To  multiply  numbers  ending  with  zeros. 

a.  When  both  numbers  are  integers.  Multiply  the  numbers 
represented  by  the  significant  figures.  To  the  product  thus  obtained^ 
annex  as  many  zeros  as  there  are  final  zeros  in  both  the  multiplicand 
and  multiplier. 

Example.     Multiply  3400  by  1200. 

Solution.  34  x  12  =  408.  Annexing  four  zeros,  we  obtain  the  product 
4,080,000. 

Perform  the  following  multiplications.  Whenever  possible,  do 
the  work  orally. 

1.    169  X  300.  2.    210  X  300. 

3.   4567  X  700.  4.    1390  x  1200. 


5.   2300x1500. 
7.    3194  X  23,000. 


.6.    19,000x16. 
8.    420  X  3400. 


b.  When  one  of  the  numbers  is  a  decimal  fraction.  Multiply 
the  numbers  represented  by  the  significant  figures.  Move  the  decimal 
point  as  many  places  to  the  right  in  the  product  as  there  are  final 
zeros  in  the  integer.     (This  may  necessitate  annexing  zeros.) 

Eza^iples. 

1.    Multiply  .486  by  300. 

Solution.  3  x  .486  =  1.458. 

Move  the  decimal  point  two  places  to  the  right,  the  result  is  145.8. 


SHORT  METHODS  31 

2.  Multiply  8.2  by  400. 

Solution.  4  x  3.2  =  12.8. 

Move  the  decimal  point  two  places  to  the  right,  the  result  is  1280. 

Written  Work 
Perform  the  following  multiplications: 
1.    .47  X  200.  2.    3.786  x  4000. 

3.  17.682  X  500.  4.    .0746  x  3000. 
5.    .072  X  6000.  6.    .382  x  1200. 
7.    .0837x14000.  8.    .042x170. 

9.    .0036  x  1500.  10.    4.26  x  7000. 

19.  To  multiply  by  9,  99,  999,  etc. 

a.  To  multiply  by  9.  Annex  one  zero  to  the  number  to  he  multi- 
plied^ thus  multiplying  it  hy  10;  from  this  result  subtract  the  num- 
ber to  be  multiplied. 

Example.     Multiply  846  by  9. 

Solution.  3460 

346 
3114 

b.  To  multiply  by  99.  Annex  two  zeros  to  the  number  to  be  mul- 
tiplied^ thus  multiplying  it  by  100;  from  this  result  subtract  the 
number  to  be  multiplied. 

Example.     Multiply  298  by  99. 

Solution.  29300 

293 
29007 

Written  Work 
Multiply  each  of  the  following  numbers  by  9,  99,  and  999 : 
1.  632.         2.  748.         3.  185.         4.  737.         5.  427.         6.  166. 

20.  To  multiply  by  numbers  slightly  smaller  than  10,  100,  1000, 
10,000,  etc. 

A  modification  of  the  short  method  explained  in  the  preceding 
section  may  be  used  to  multiply  by  numbers  slightly  smaller  than 
10,  100,  1000,  10,000,  etc. 


32  MULTIPLICATION 

To  multiply  by  98.     Annex  two  zeros  to  the  number  to  he  multi- 
'plied  and  from  this  result  subtract  twice  the  number  to  be  multiplied. 

How  can  the  short  method  be  used  if  you  are  to  multiply  by 
97,  96,  95,  or 


Written  Work 
Apply  short  methods  to  the  following  examples: 

1.    675  X  96.  2.    350  x  95.  3.  535  x  91. 

4.    687  X  97.  5.    94  x  3.4.  6.  995  x  82. 

7.    634  X  994.  8.    .48  x  997.  9.  23  x  99. 

10.    48  X  997.  11.    12  x  988.  12.  47  x  998. 

21.    To  multiply  by  11. 

a.  When  the  multiplicand  contains  two  digits. 
Place  between  these  two  digits^  their  sum. 

Example.     34  x  11  =  374. 

When  the  sum  of  the  two  digits  is  10  or  more,  1  must  be  carried 
to  the  digit  at  the  left. 

Example.     68  x  11  =  748. 

Written  Work 
Multiply  each  of  the  following  numbers  by  11: 

1.    27.  2.    63.         3.    93.         4.    74.         5.    26.         6.    35. 

7.    22.  8.    87.         9.    28.       10.    46.       ii.    75.        12.    96. 

13.    37.       14.    36.       15.    57.       16.    85.       17.    98.        18.    72. 

b.  When  the  multiplicand  contains  three  or  more  digits: 

The  units'  digit  of  the  multiplicand  is  the  units'  digit  of  the  prod  • 
uct;  the  sum  of  the  units'  and  tens'  digits  is  the  tens'  digit  of  the 
product ;  the  sum  of  the  tens'  and  hundreds'  digits  is  the  hundreds' 
digit  of  the  product.,  etc. 

Whenever  the  sum  of  two  digits  is  ten  or  more,  1  must  be  carried. 


SHORT  METHODS  33 

Examples.     1.    Multiply  793  by  11. 

Solution.  3  (the  units'  digit  of  the  multiplicand)  becomes  the 

units'  digit  of  the  product. 
9  4-  3  =  12  (carry  the  1) 

1  +  7  +  9  =  17  (carry  the  1) 

1  +  7=    8 

8723 

2.    Multiply  52,635  by  11. 

Solution.  52,635  x  11'=  578,985. 

Written  Work 
Multiply  each  of  the  following  by  11: 

1.    363.  2.  271. 

3.    823.  4.  456. 

5.    3742.  6.  876,394. 

7.    3,578,962.  .  8.  34,579. 

9.    263,789.  10.  123,496,287. 

22.    To  multiply  by  111. 

362,941x111=? 

When  the  multiplication  is  performed  in  the  customary  manner, 
the  multiplicand  is  repeated  as  follows: 

362941 
362941 
362941 

When  the  short  method  is  applied,  the  units'  digit  of  the  multi- 
plicand i&  the  units'  digit  of  the  product ;  the  sum  of  the  units'  and 
tens'  digits  of  the  multiplicand  is  the  tens'  digit  of  the  product ;  the 
sum  of  the  units'^  tens' ^  and  hundreds'  digits  of  the  multiplicand  is  the 
hundreds'  digit  of  the  product;  the  sum  of  the  tens\  hundreds'^  and 
thousands'  digits  of  the  multiplicand  is  the  thousands'  digit  of  the 
products  etc. 

The  excess  above  10  is  always  to  be  carried  to  the  next  sum. 


34  MULTIPLICATION 

Written  Work 

Without  recopying,  write  the  products  obtained  by  multiplying 
each  of  the  following  by  111: 

1.  729,361.  2.    124,396.  3.    1,793,862. 
4.    5,374..                         5.    235,692.  6.    8,354,927. 

23.    To  multiply  two  numbers  ending  in  5. 

a.  When  the  sum  of  the  digits  at  the  left  of  the  5's  is  an  even 
number. 

Multiply  the  digits  at  the  left  of  the  o's  ;  to  this  product  add  one 
half  the  sum  of  these  digits  ;  to  this  result  annex  25. 

Examples.     1.    Multiply  Q5  by  25. 

Solution.    2  x  6  =  12,  the  product  of  the  digits  at  the  left  of  the  5's. 
i  of  (2 +  6)=  J 
16 
1625,  result  obtained  by  annexing  25. 

2.  Multiply  625  by  445. 

.  Solution.    62  x  44  =  2728 
I  of  (62  +  44)  =      53 
2781 
278125,  result  obtained  by  annexing  25. 

Written  Work 
Multiply  as  indicated: 

1.    35  X  75.  2.  95  X  75. 

3.    35  X  55,  4.  25  X  45. 

5.    325  X  45.  6.  725  x  65. 

7.    835x175.  8.  145x165; 

9.    195x115.  10.  225x185. 

h.  When  the  sum  of  the  digits  at  the  left  of  the  5's  is  an 
odd  number. 

Multiply  the  digits  at  the  left  of  the  5'8  ;  to  this  product  add  one 
half  the  sum  of  these  digits^  dropping  the  I  ;  to  this  result  annex  75. 


SHORT  METHODS  35 

Examples.     1.    Multiply  75  by  45. 

Solution.     4x7  =  28,  the  product  of  the  digits  at  the  left  of  the  5*s. 
i  of  (4  +  7)  =  Jl 

3375,  the  result  obtained  by  dropping  the  fraction  I,  and  annexing  75. 

2.    Multiply  325  by  475. 

Solution.  32  x  47  =  1504 

^  of  (32 +47)=      391, 

1543,  adding  and  dropping  the  I. 
154,375,  result  secured  by  annexing  75. 

Written  Work 
Multiply  as  indicated: 

1.    75x65.  2.    125x135. 

3.    95  X  85.  4.    145  X  175. 

5.    225  X  75.  6.    165  x  135. 

7.    145  X  215.  8.    435  x  125. 

24.  To  multiply  two  numbers,  when  certain  digits  of  the  multi- 
plier are  contained  an  integral  number  of  times  in  other  digits  of  the 
multiplier. 

Multiply  224  by  279. 

Since  9  is  contained  3  times  in  27,  first  multiply  224  by  9,  then 
multiply  this  product  by  3. 
Thus,  224 

279 
2016  =  9x224 
6048    =3x2016 
62496 
When  using  this  method,  be  careful  to  place  the  product  of  the 
second  multiplication  in  the  proper  position. 

Example.     1.    Multiply  341  by  618. 

341  Solution.     Since  18  is  a  multiple  of  6,  multiply 

g;[g  first  by  6.     Place  the  right-hand  figure  of  the  product, 

904^       _  a       qj.1  2046,  directly  under  the  6  of  the  multiplier.     The  prod- 

"~      •  net  of  18  X  341  can  now  be  obtained  by  multiplying 

__6138  =  3  X  2046  2046  by   3.     The  right-hand  figure  of  this  product, 

210738  6138,  is  placed  directly  under  the  8  of  the  multiplier. 


36  MULTIPLICATION 

Written  Work 

.    Multiply  the  following,  stating  by  Avhat  numbers  you  multiplied 
in  order  to  take  advantage  of  the  short  method: 

1.    468  X  243.  2.   1,235  x  981.  3.    719  x  427. 

4.    687  X  654.  5.    739  x  848.  6.    7,362  x  1,248. 

7.    1,247  X  1,864.  8.    146,387  x  315.         9.    1,235  x  819. 

25.  The  supplement  of  a  number  is  the  difference  between  the 
number  and  the  next  lower  power  of  10.  The  supplement  of  15 
is  5  ;  the  supplement  of  134  is  34 ;  the  supplement  of  1042  is  42. 

26.  To  multiply  two  numbers  each  of  which  is  a  little  larger 
than  100. 

To  either  of  the  numbers  add  the  supplement  of  the  other;  to  this  sum 
annex  the  product  of  the  supplemerits. 

Example.     Multiply  131  by  103. 

Solution.  131  +  3  =  134 

(or  103  +  31  =  134). 
Annex  93  (31  x  3). 
The  result  is  13,493. 

The  same  rule  may  be  applied  to  numbers  a  little  larger  than 
1000. 

Example.     Multiply  1,062  by  1,006. 

Solution.  1062  +  6  =  1068 

62  X  6  = ^72 

1068372 

Note.  When  the  supplements  are  based  on  100  and  the  product  of  the  supple- 
ments is  a  number  of  only  one  digit,  a  zero  must  be  put  in  tens'  place.  For 
example  :  102  x  103  =  10,506.  Similarly,  when  the  supplements  are  based  on  1000 
and  the  product  of  the  supplements  is  a  number  of  less  than  three  digits,  zeros  must 
be  put  in  the  proper  places. 

Written  Work 

1.    104  X  120.  2.    127  X  102.  3.  113  x  106. 

4.    114  x  105.  5.    114  X  106.  6.  109  x  106. 

7.    126  x  107.  8.    109  x  111.  9.  1,007  x  1,003. 


SHORT  METHODS  37 

10.  1,009  X  1,012.  11.  1,214  X  1,006.  12.  1,206  x  1,012. 
13.  1,112x1,006.  14.  1,416x1,009.  15.  1,374x1,005. 
16.    1,674x1,012. 

27.  The  complement  of  a  number  is  the  difference  between  the 
next  higher  power  of  10  and  the  number.  The  complement  of  92 
is  8 ;  the  complement  of  89  is  11 ;  the  complement  of  996  is  4. 

28.  To  multiply  two  numbers  both  slightly  less  than  100. 

From  either 'number  subtract  the  complement  of  the  other  number. 
To  this  result  annex  the  product  of  the  complements. 

Example.     Multiply  96  by  93. 

Solution.         96  -  7  =  89  (or  93  -  4  =  89). 

4  X  7  =  28  (product  of  the  complements). 

Annex  28  to  89  and  the  result  is  8928. 

Note.  When  the  complements  are  based  on  100  and  the  product  of  the  comple- 
ments is  less  than  10,  a  zero  must  be  put  in  tens'  place.  For  Illustration :  98  x  97  = 
9506.  Similarly,  the  tens'  and  hundreds'  places  must  be  filled  when  the  complements 
are  based  on  1000. 

Written  Work 

Multiply  as  indicated.  Perform  orally  as  much  of  this  work  as 
possible. 

1.    98  X  95.  2.    97  X  84.  3.    87  x  91. 

4.    95x80.  5.    93x85.  6.    87x97. 

7.    88  X  87.  8.    91  X  92.  9.    86  x  94. 

The  same  method  may  be  applied  to  numbers  slightly  less  than 
1000. 

Example.     Multiply  996  by  987. 

Solution.     996-13  (the  complement  of  987)  =  983. 

4  X  13  =  52  (the  product  of  the  complements). 

Since  the  complements  are  based  on  1000  and  the  product  of  the  comple- 
ments is  a  number  of  only  two  digits,  a  zero  must  be  put  in  hundreds*  place. 
The  result  is  983,052. 


38 

MULTIPLICATION 

Multiply  : 

Written  Work 

1.    994 

2.    996 

3.    983 

4.    987 

992 

984 

991 

992 

5.    991 

6.    983 

7.    978 

.     8.    981 

981    • 

982 

983 

988 

29.    To  multiply  any  two  numbers  in  the  teens. 

To  either  of  the  nmnbers  add  the  units'  digit  of  the  other  number  and 
annex  a  zero. 

To  this  result  add  the  product  of  the  units'  digits. 

Example.     Multiply  15  by  17. 


Solution. 

15  +  7  = 

:  22  ' 

;  annex  a  zero,  220 

255 

Oral  Work 

Multiply 
1.   17 
12 

2.    13 

12 

3.   16 

18 

4.    17 

13 

5.   14 
13 

6. 

19 
15 

7.  13 
16 

8.  17 
19 

9.   18 
12 

10.  13 
19 

11.  17 

16 

12. 

15 
17 

CHAPTER   IV 


DIVISION 


Oral  Work 

30.    Short  Division. 

1.  Divide  by  2  :  16,  28,  76,  248,  368,  926,  1,054. 

2.  Divide  by  3  :  27,  eS6,  57,  75,  417,  732,  873. 

3.  Divide  by  4  :  32,  48,  64,  72,  96,  196,  384,  748. 

4.  Divide  by  5  :  75,  95,  145,  545,  725,  965,  1,025,  1,370. 

5.  Divide  by  6  :  72,  96,  126,  366,  528,  732,  1,044. 

6.  Divide  by  7  :  36,  91,  147,  203,  476,  924,  1,575. 

7.  Divide  by  8  :  72,  96,  144,  360,  424,  792,  1,240. 

8.  Divide  by  9  :  54,  98,  171,  243,  378,  567,  981. 

State  the   remainder  when  each  of   the    following  numbers  is 
divided  by  3,  4,  5,  7,  8,  and  9. 

9.  10.  11. 

473  9,846  2,638 

692  3,723  7,284 

876  9,264  3,047 

479  3,749  2,636 

14.  How  many  pounds  of  meat  can  be  bought  for  $1.26  at  18^ 
per  pound  ? 

15.  How  many  weeks  in  91  days?     175  days  ?     266  days  ? 

16.  The  dividend  is  176  and  the  quotient  is  8.     What  is  the 
divisor  ? 

17.  The  divisor  is  9,  the  quotient  is  7,  and  the  remainder  is  3. 
What  is  the  dividend  ? 

18.  Six  dozen  oranges  were  bought  for  S  1.62.     What  was  the 
price  per  dozen? 

19.  How  many  yards  in  186  feet  ?     924  feet  ?     5280  feet  ? 

39 


12. 

13. 

4,020 

19,206 

7,302 

47,308 

7,960 

23,074 

8,403 

95,306 

40  DIVISION 

20.  A  grocer  buys  9  dozen  eggs  for  $2.07.     What  is  the  cost 
per  dozen  ? 

21.  If  you  are  to  discharge  a  debt  of  <f  1.14  in  6  equal  weekly 
payments,  how  much  must  you  pay  each  week  ? 

31.    Long  Division. 

Examples.     1.  Divide  4,625  by  37.     2.    Divide  47,285  by  327. 
125  144i|f 

Solution.     37  1 4625  Solution.     327  [47285 

37  327 

92  1458 

74  •  1308 


185  1505 

185  1308 


197 
(The  quotient  should  be  written  above  the  dividend  in  long 
division.) 

32.    Checks.     Division   may  be   checked   by   several   methods. 
The  method  stated  below  is  easily  understood  and  readily  applied. 

Multiply   the   quotient   by  the  divisor  and  add  the  remainder  to  thi^ 
product  to  obtain  the  dividend. 

Written  Work 
Perform  the  following  divisions  and  check  each  result: 
1.    1,758-^144.  2.    15,762-^37. 

3.    73,627-5-425.  4.    78,264 -- 738. 

5.    508,573-^97.  6.    66,816^928. 

7.    41,228-^-44.  8.    2,235,812^284. 

9.    Divide  the  sum  of  478,  392,  648,  971,  and  1483  by  27. 

10.  Divide  the  sum  of  3024,  4763,  8297,  9468,  and  293  by  38. 

11.  Complete  :  37  x  29  = 

42x29  = 
36  X  29  = 
94  X  29  = 

402x29  = 

Total  = 


DIVISION  41 

12.  The  total  circulation  of  a  certain  daily  newspaper  for  23 
consecutive  days  was  524,423  copies.  What  was  the  average  daily 
circulation  ? 

13.  At  i2.18  a  yard,  how  many  yards  of  cloth  can  be  bought 
for  $37.06? 

14.  The  dividend  is  14,286,  the  quotient  is  18,  and  the  remain- 
der is  12.     What  is  the  divisor? 

15.  The  product  of  two  numbers  is  135,468.  One  of  the  num- 
bers is  426.     What  is  the  other? 

16.  In  a  factory  437  men  produce  5681  articles  in  a  week. 
What  is  the  average  weekly  production  for  each  employee  ? 

17.  At  the  rate  of  43  miles  an  hour,  how  long  will  it  take  a 
train  to  run  473  miles  ? 

18.  Into  how  many  states  as  large  as  Rhode  Island  (1067  sq. 
mi.)  could  Texas  (262,398  sq.  mi.)  be  divided? 

19.  The  expenses  for  5  months  for  a  family  of  5  amounted  to 
$258  for  food,  |170  for  rent,  $216  for  clothes,  §147  for  amuse- 
ments  and  other  expenses.  What  was  the  average  expense  a  month 
for  the  family  and  the  average  per  month  for  each  person  ? 

33.  Pointing  Off  the  Quotient.  When  it  is  necessary  to  continue 
a  division  to  tenths  or  hundredths,  place  a  decimal  point  to  the 
right  of  the  units'  figure  of  the  dividend  and  the  quotient,  annex 
zeros  to  the  dividend,  and  continue  the  process. 

Example.     Divide  2916  by  26. 

112.1 


Solution.  26  2916.0 


Written  Work 

The  following  table  gives  the  area  of  each  of  the  states  in  square 
miles,  and  also  the  population  of  each  state. 

Review  the  instructions  given  on  page  9  for  ruling  a  blank 
form  and  for  entering  statistics. 


42  DIVISION 

Prepare  a  form  similar  to  the  following : 


State  and  Division 


New  England 

Maine 

New  Hampshire  .     .     . 

Vermont 

Massachusetts  .  .  . 
Rhode  Island  .... 
Connecticut     .... 

Middle  Atlantic 
New  York        .     .     .     .     , 
New  Jersey      .     .     .     .     . 
Pennsylvania 

East  North  Central 

Ohio 

Indiana , 

Illinois 

Michigan 

Wisconsin , 

West  North  Central 

Minnesota 

Iowa 

Missouri 

North  Dakota      .     .     .     . 
South  Dakota       .     .     .     . 

Nebraska 

Kansas 

South  Atlantic 

Delaware 

Maryland 

D.  C 

Virginia 

West  Virginia 

North  Carolina     .     .     .     . 
South  Carolina     .     .     .     . 

Georgia 

Florida 

East  South  Central 

Kentucky 

Tennessee 

Alabama 

Mississippi 


Land  Area  in 

Population 

Population  per 

Square  Miles 

1910 

Square  Mile 

29,895 

742,371 

9,031 

430,572 

9,124 

355,956 

8,039 

3,366,416 

1,067 

542,610 

4,820 

1,114,756 

47,654 

9,113,614 

7,514 

2,537,167 

44,832 

7,665,111 

40,740 

4,767,121 

36,045 

2,700,876 

56,043 

5,638,591 

57,480 

2,810,173 

55,256 

2,333,860 

80,858 

2,075,708 

55,586 

2,224,771 

68,727 

3,293,335 

70,183 

577,056 

76,868 

583,888 

76,808 

1,192,214 

81,774 

1,690,949 

1,965 

202,322 

9,941 

1,295,346 

60 

331,069 

40,262 

2,061,612 

24,022 

1,221,119 

48,740 

2,206,287 

30,495 

1,515,400 

58,725 

2,609,121 

54,861    . 

752,619 

40,181 

2,289,905 

41,687 

2,184,789 

51,279 

2,138,093 

46,362 

1,797,114 

DIVISION 


43 


State  and  Division 


Land  Area  in 
Square  Miles 


Population 
1910 


Population  per 
Square  Mile 


West  South  Central 

Arkansas     

Louisiana 

Oklahoma 

Texas 

Mountain 

Montana 

Idaho      

Wyoming 

Colorado 

New  Mexico    .... 

Arizona 

Utah 

Nevada  

Pacific 
Washington     .... 

Oregon   

California 


52,525 

45,409 

69,414 

262,398 


146,201 

83,354 

97,594 

103,658 

122,503 

113,810 

82,184 

109,821 


66,836 

95,607 

155,652 


1,574,449 
1,678,339 
1,657,155 
3,896,542 


376,053 
325,594 
145,965 
799,024 
327,301 
204,354 
373,351 
81,875 


1,141,990 

672,765 

2,377,549 


Note.  The  class  may  be  divided  into  groups  and  each  group  made  responsible 
for  a  geographical  division. 

Complete  as  much  of  the  table  as  the  teacher  assigns,  showing 
the  population  per  square  mile  of  each  state,  of  each  section,  and 
of  the  United  States. 

Carry  results  to  one  decimal  place. 

Exercises  for  Drill 


I.   Estimated  Time  7  Minutes 


1.  Add: 

a,             h. 

c. 

d. 

e. 

/. 

9- 

h. 

27     14 

29 

73 

29 

83 

72 

94 

36     33 

43 

99 

48 

92 

^  86 

55 

92     27 

38 

26 

73 

17 

93 

76 

23     19 

64 

10 

27 

64 

14 

87 

49     86 

27 

18 

65 

20 

27 

31 

85     35 

85 

35 

42 

78 

38 

49 

44 


DIVISION 


2.    Multiply : 


a. 
4786 
3 


5. 
9463 
5 


c. 

7427 
8 


3.    Subtract: 

a. 

h. 

c. 

d. 

72049 

4706 

32964 

92807 

32608 

2985 

7193 

1968 

4.    Add  across  and  down 
a. 

7+3+9+2= 
5+4+8+3= 
4+5+1+9= 
7+6+5+1= 
1+9+3+4= 
8+1+2+5= 
3+2+7+8= 

9_+7  +  4+6=_ 

+     +     +     = 


24+  7  +  6 
13+  5  +  3 
17+    4  +  7 

9  +  15  +  3 
18+  9  +  5 
13+    2  +  1 

7  +  19  +  8 

15  +  _3  +  9^ 

+       + 


11.   Estimated  Time  9  Minutes 
1.    Add  across  and  down : 

741+437  +  563  +  234 
526  +  318  +  725  +  238 
382  +  746  +  128  +  407 
387  +  209  +  504  +  916 
328  +  460  +  937  +  659 
473  +  295  +  243  +  175 


+ 

+ 

+ 

2.    Multiply: 

a. 

h. 

c. 

d. 

7460 

9047 

739 

7036 

38 

29 

86 

43 

DIVISION 


45 


3. 


4.    Divide; 


143  X  6  = 
427  X  5  = 

793  X  8  = 
429  X  7  = 
384  X  3  = 
827  X  6  = 
538  X  9  = 


326   6846 


22  6996 


III.     Estimated  Time  8  Minutes 


Add  across  and  down  : 


7 

9 

7 

3 

5 

8 

1            8 

4 

2 

5 

9 

2 

4 

7            3 

3 

8 

3 

6 

4 

5 

3            6 

6 

4 

7 

7 

8 

9 

8            9 

2 

3 

9 

4 

7 

T 

6            7 

9 

5 

8 

8 

9 

6 

4            2 

8 

7 

6 

5 

3 

3 

5            4 

4 

6 

4 

1 

1 

4 

9            8 

7 

1 

9 

2 

2 

1 

2            5 

6 
Subl 

9 

bract  : 
a. 

2 

8 

5. 

6 

2 

7            1 

74036 

92407 

769082 

21809 

38795 

432767 

Multiply  : 

a. 

h. 

c- 

3742 

9427 

3897 

37 

4£ 

J 

28 

Divide  : 

a. 

5. 

6[ 

748632 

81938424 

46 


DIVISION 


IV.     Estimated  Time  8  Minutes 


1.   Add 


a.            b. 

c. 

d. 

e. 

/. 

9- 

h. 

37          24 

33 

51 

26 

72 

43 

13 

24          13 

15 

32 

39 

46 

75 

37 

36          43 

31 

44 

72 

92 

76 

11 

15          25 

17 

65 

43 

54 

28 

26 

13          17 

Q5 

23 

86 

28 

35 

34 

11          38 

22 

25 

54 

63 

54 

82 

.    Subtract : 

a. 

h. 

c. 

d. 

4372 

7246 

) 

9264 

i 

5164 

2439 

3817 

5728 

1476 

3.    Add  from  left  to  right 


a. 


b. 


7+3+2+4= 
3+7+5+6= 
4+8+9+1= 
3+7+2+4= 
8+3+7+5= 
9+3+2+8= 
5+7+3+8= 

6+9+4+8= 
13  +  17  +  19  +  12  = 
15  +  13  +  12  +  16  = 

5+7+8+6= 

13  +  27  +  32  +  17  = 

48  +  27  +  3  +  2  = 

7+9+2+3= 

4.    Multiply: 
a. 

b. 

c.                        d. 

3724 
2 

4923 
3 

6728                   3107 
2                        3 

V.     Estimated  Time  12  Minutes 

1.    Divide  : 

a. 

b. 

c. 

5|  742385 

8|  948824 

91736848 

DIVISION 

2.    Multiply : 

a. 

5. 

c. 

1437 
246 

1943 
632 

1048 
453* 

3.    Subtract : 

a. 

5. 

c. 

d. 

472,387 
29,389 

940,360 

397,685 

472,863 
30,940 

796,048 
397,059 

47 


4.  Add  across  and  down: 

943  +  790  +  408  +  941  = 
276  +  463  +  312  +  806  = 
841  +  287  +  637  +  420  = 
732  +  934  +  924  +  387  = 

286  +  742  +  836  +  209= 

+    +    +    = 

5.  Divide: 

a,  h, 

» 

423|13536  91|46228 

Computing  Machines  of  various  kinds  are  generally  used  by  banks  and 
other  business  houses.  Machines  on  which  addition,  subtraction,  multiplica- 
tion, and  division  may  be  performed  are  quite  common. 


CHAPTER  V 
AVERAGE 

34.  Simple  Average.  A  boy  walked  9  miles  on  Monday,  5  miles 
on  Tuesday,  and  10  miles  on  Wednesday.  If  he  had  divided  the 
trip  into  three  equal  distances,  how  many  miles  would  he  have 
walked  each  day  ?  In  other  words,  what  was  the  average  distance 
walked  each  day  ? 

A  man  owned  a  five-acre  field.  One  acre  yielded  71  bushels  of 
potatoes,  another  77  bushels,  a  third  85  bushels,  the  fourth  93 
bushels,  and  the  fifth  64  bushels.  What  was  the  total  crop? 
What  was  the  average  crop  per  acre  ? 

What  two  processes  are  usually  involved  in  computing  an 
average  ? 

Written  Work 

1.  'The  noon  temperatures  in  a  certain  city  for  a  week  were  as 
follows;  Monday,  62°;  Tuesday,  70°;  Wednesday,  74°;  Thurs- 
day, 68°;  Friday,  62°;  Saturday,  70°;  Sunday,  76°.  What  was 
the  average  noon  temperature  for  the  week  ? 

2.  A  newsdealer  sold  papers  as  indicated  in  the  table.  Find 
the  average  number  of  each  sold. 


MON. 

TUES. 

Wed. 

Thurs. 

Fri. 

Sat., 

AVG. 

Sentinel  .  .  . 

39 

47 

63 

82 

74 

67 

Argus  .... 

13 

19 

27 

31 

29 

26 

Tribune  .  .  . 

39 

42 

48 

51 

39 

41 

Recorder  .  .  . 

28 

43 

56 

29 

37 

29 

3.  The  following  table  gives  the  prices  received  by  farmers  in 
certain  states  for  the  butter  sold  during  the  months  of  a  recent 
year.  Find  the  average  price  received  in  each  state  during  the 
year. 

.48 


AVERAGE 


49 


Butter  Prices  in  Certain  States 


Cents  per  Pound 

Average 
Price 

BY 

States 

i 

4 

1 

1 

^ 

§ 

t 

3 

i 

i 

1 

i 

>-> 

fe 

1 

< 

S 

>-» 

^ 

< 

m 

o 

;? 

^ 

Massachus 

3tts    37 

38 

36 

35 

33 

34 

31 

33 

34 

34 

32 

35 

Rhode  Isla 

nd.    35 

39 

39 

34 

34 

36 

32 

32 

35 

34 

34 

34 

Connecticu 

t    .     36 

39 

38 

35 

34 

35 

33 

34 

34 

36 

34 

36 

New  York 

.     .    34 

35 

32 

31 

31 

30 

27 

29 

29 

30 

32 

35 

New  Jersej 

r      .     37 

40 

35 

34 

34 

34 

32 

32 

33 

32 

34 

36 

Pennsylvar 

lia      33 

35 

33 

31 

31 

29 

26 

27 

28 

30 

32 

34 

Maryland  . 

.    28 

29 

29 

28 

25 

25 

25 

25 

26 

28 

29 

28 

Virginia 

.     .    25 

26 

26 

26 

25 

23 

21 

22 

22 

24 

26 

26 

West  Virgi 

oia     26 

26 

26 

26 

26 

22 

21 

21 

22 

24 

25 

27 

Georgia 

.     .    25 

25 

28 

24 

24 

24 

24 

24 

24 

25 

25 

26 

Ohio       . 

.     .     27 

28 

27 

25 

25 

24 

22 

23 

24 

25 

27 

29 

Indiana 

.     .    25 

26 

25 

24 

24 

22 

21 

22 

22 

24 

25 

27 

Illinois . 

.     .    27 

28 

26 

25 

25 

24 

24 

23 

24 

26 

26 

28 

Michigan 

.     .    30 

31 

28 

27 

27 

25 

23 

23 

24 

25 

27 

29 

Wisconsin 

.    33 

34 

28 

28 

29 

26 

25 

25 

26 

.27 

28 

31 

Minnesota 

.    31 

32 

29 

27 

27 

27 

24 

24 

25 

26 

28 

30 

Iowa 

.     29 

30 

27 

26 

26 

25 

24 

24 

24 

25 

27 

29 

Missouri 

.    23 

23 

23 

23 

23 

22 

21 

21 

21 

22 

23 

24 

Nebraska  . 

.     26 

26 

24 

24 

23 

22 

21 

21 

22 

23 

25 

27 

Kansas 

.     26 

26 

25 

24 

24 

22 

21 

22 

22 

24 

25 

26 

Kentucky 

.    21 

22 

21 

21 

21 

21 

19 

19 

18 

20 

20 

23 

Tennessee 

.    21 

22 

21 

20 

20 

19 

18 

18 

18 

19 

20 

22 

Louisiana  . 

.    28 

30 

28 

27 

28 

27 

26 

27 

27 

27 

28 

30 

Texas     . 

.     .    22 

25 

23 

22 

21 

21 

21 

20 

21 

23 

23 

24 

Oklahoma 

.    27 

25 

23 

22 

22 

22 

20 

20 

19 

23 

24 

25 

Montana 

.    36 

37 

35 

33 

31 

31 

30 

29 

31 

31 

32 

35 

Colorado 

.    33 

33 

30 

30 

28 

28 

26 

26 

28 

28 

32 

31 

Utah      . 

.    33 

31 

30 

29 

31 

30 

29 

27 

28 

30 

32 

32 

Idaho     . 

.    35 

33 

32 

32 

31 

28 

28 

27 

29 

31 

32 

34 

Washingtoi 

1    .    36 

37 

32 

32 

30 

28 

28 

30 

30 

32 

33 

35 

Oregon  . 

.    34 

35 

33 

32 

31 

26 

28 

28 

30 

30 

35 

36 

Oalifornia 

.    34 

36 

34 

32 

30 

29 

20 

31 

31 

33 

34 

36 

4.  The  following  table  gives  the  acreage  planted  to  certain 
crops  in  the  United  States,  and  the  crops  raised.  Compute  the 
average  yield  per  acre.  Carry  your  results  to  two  decimal  places. 
Show  the  statistics  on  a  ruled  form. 


50 


AVERAGE 


Acreage  and  Production   of   Crops 


Crop 

1911 

1912 

1000  Acres 

1000  Bushels 

Bushels  per 
Acre 

1000  Acres 

1000  Bushels 

Bushels  per 
Acre 

Corn      .     . 
Wheat  .     . 
Oats      .     . 
Rye  .     .     . 
Potatoes     . 

105,825 

49,543 

37,763 

2,127 

3,619 

2,531,488 

621,338 

922,298 

33,119 

292,737 

107,083 

45,814 

37,917 

2,117 

3,711 

3,124,746 
730,267 

1,418,337 

35,664 

420,647 

5.    The    following  table  shows  the  number  of   cases  of  eggs 
shipped  to  seven  leading  markets  iri  the  United  States. 


Receipts  of  Eggs  at  Seven  Leading  Markets  in  the  United  States 

1906-1912 


Year 

Boston  . 

Chicago 

Cincin- 
nati 

Mil- 
waukee 

New 
York 

St.  Louis 

San 
Francisco 

Total 

1906  ...     . 

1907  .... 

1908  .... 

1909  .... 

1910  .... 

1,709,531 
1,594,576 
1,436,786 
1,417,397 
1,431,686 

3,583,878 
4,780,356 
4,569,014 
4,557,906 
4,844,045 

484,208 
588,636 
441,072 
519,652 
511,519 

187,561 
176,826 
207,558 
160,418 
169,448 

3,981,013 
4,262,153 
3,703,990 
3,903,867 
4,380,777 

1,023,125 
1,288,977 
1,439,868 
1,395,987 
1,375,638 

137,074 
379,429 
347,436 
340,185 
469,698 

Av.  1906-1910 

1911  .... 

1912  .... 

1,441,748 
1,580,106 

4,707,335 
4,556,643 

605,131 
668,942 

175,270 
136,621 

5,021,757 
4,723,558 

1,736,915 
1,391,611 

587,115 
6:i8,920 

Av.  1911-1912 

Find  (1)  the  total  receipts  of  eggs  each  year,  (2)  the  average 
receipts  at  each  city  for  the  periods  indicated. 

6.    A  subscription  was  taken  to  secure  funds  to  purchase  a  gift. 

3  men  gave  $1.00  each 

1  man  gave       .75 

2  men  gave     1.50  each 
1  man  gave       .60 

4  men  gave       .90  each 
Find  the  average  amount  given. 


AVERAGE 


51 


7.  The  following  table  shows  the  number  of  men  employed  and 
the  total  weekly  wages  in  each  of  the  four  departments  of  a 
faccory.  Find  the  average  wage  in  each  department  and  the 
average  wage  for  the  four  departments. 


Department 


Number  of  Men 
Employed 


47 
18 
62 
26 


Total  Wage 


I  960 

290 

1054 

318 


Average  Wage 


Oral  Review 

1.  What  is  the  difference  in  the  meaning  of  the  following  state- 
ments ? 

a.  Each  of  the  300  employees  in  our  factory  earns  $2.50  per 
day. 

b.  The  average  daily  wages  of  employees  in  our  factory  is  f  2.50 
per  day. 

2.  What  would  you  have  to  know  and  how  would  you  proceed 

to  find  : 

a.  The  average  weight  of  twenty  boxes? 

b.  The  average  value  of  a  herd  of  cattle  ? 

c.  The  average  number  of  miles  a  train   traveled   per   hour, 
going  from  Chicago  to  St.  Louis  ? 

d.  The  average  age  of  the  students  in  your  class  ? 

e.  The  average  daily  sales  of  a  clerk  ? 

3.  What  could  you  find  if  you  were  told: 

a.  The  average  value  of  farm  land  per  acre  in  your  state,  and 
the  number  of  acres  of  farm  land  ? 

b.  The  average  daily  sales  of  a  clerk  during  the  twenty-five 
week  days  of  June  ? 

c.  The  average  monthly  grocery  bill  of  your  family  ? 


52  AVERAGE 

4.  If  you  were  told  : 

a.  The  daily  circulation  of  the  Evening  Herald  for  the  twenty- 
six  week  days  of  July,  and  the  average  daily  circulation  of  the 
Evening  Transcript  for  the  same  month,  how  could  you  compare 
their  circulation  ? 

h.  The  average  daily  wages  of  A,  who  worked  265  days  last 
year  and  the  average  dail}^  wages  of  B,  who  worked  303  days, 
how  could  you  find  the  yearly  wages  of  each,  and  which  one 
earned  the  larger  amount  ? 

c.  The  difference  between  the  average  daily  outputs  of  two  shoe 
factories,  how  could  you  find  the  difference  in  their  production 
for  a  year  of  300  working  days  ? 

5.  What  would  you  have  to  know  and  what  would  you  do  to 
find  the  average  daily  speed  of  an  ocean  liner  on  a  given  voyage  ? 

6.  Several  boys  worked  for  a  farmer  picking  strawberries. 
One  earned  $5.00  more  than  the  average  of  the  other  boys' 
earnings.  What  else  must  you  know  and  what  would  you  do  to 
find  the  total  earnings  of  all  the  boys  ?  What  else  would  you 
have  to  know  and  how  would  you  find  the  average  wage  cost  of 
picking  a  quart  of  strawberries  ? 

Written  Work 

1.  A  merchant  kept  a  record  of  the  deliveries  of  goods  made  to 
his  customers  for  a  week.     The  record  follows; 

Day  Dblivebies  • 

Monday  213 

Tuesday  187 

Wednesday  208 

Thursday  221 

Friday  168 

Saturday  251 

a.    What  was  the  average  number  of  deliveries  per  day  ?     ' 
h.    The  expense  of  running  the  delivery  wagons  for  a  week,  in- 
cluding care  of  horses,  interest  on  the  money  invested  in  horses 
and    wagons,   repairs   and  wages,   was   $64.75.     What   was  the 
average  cost  per  delivery  ? 


AVERAGE  53 

2.  Five  clerks  in  a  store  sold  the  following  amounts  of  goods 
during  a  month: 

A.  $1246.50 

B.  1076.85 
'        C.    944.90 

D.  1388.20 

E.  1109.75 

a.    What  was  the  average  amount  of  sales  per  clerk  ? 
h.    Which  clerks  sold  more  than  the  average  ?     Which  clerks 
sold  less  than  the  average  ? 

3.  The  distance  from  Chicago  to  Aurora,  Illinois,  via  the 
C.  B.  &  Q.  Railroad,  is  37.4  miles.  Train  No.  55  makes  no  stops 
between  these  stations.  It  leaves  Chicago  at  6:10  p.m.  and 
arrives  at  Aurora  at  7  :  10  p.m.  How  many  miles  an  hour  does 
this  train  travel  ?  What  fractional  part  of  a  mile  does  it  run  in 
one  minute  ? 

4.  The  single  fare  between  these  two  stations  is  74  cents.  Ten- 
trip  tickets  may  be  purchased  for  $6.25.  What  is  the  saving  in 
fare  per  trip  ? 

5.  A  25-trip  ticket  may  be  purchased  for  $13.00.  What  is  the 
average  cost  per  trip  ? 

6.  The  following  table  shows  the  number  and  value  of  pianos 
and  organs  manufactured  in  the  United  States  in  1904  and  1909. 

Pianos  1909  1904 

Number  261,197  374,154 

Value  $41,476,479  $59,501,225 


Obgans 

Number 

113,065 

64,111 

Value 

$4,162,053 

$  2,595,429 

What  was  the  average  value  of  a  piano  manufactured  in  each  of 
the  years  ? 

What  was  the  average  value  of  an  organ  manufactured  in  each 
of  the  years  ? 


54  AVERAGE 

7.  In  1900  the  population  of  the  United  States  was,  in  round 
numbers,  77  million.  The  combined  daily  circulation  of  all  daily 
newspapers  was  about  15  million  copies;  an  average  of  1  copy  of 

a  daily  paper  to  every persons.     In  1910  the  population  had 

increased  to  93  million,  and  the  circulation  of  daily  newpapers  to 
24  million,  or  an  average  of  one  copy  for  every persons. 

8.  During  the  year  1913  the  United  States  Congress  appro- 
priated $1,098,678,788  for  the  expenses  of  the  government.  The 
last  preceding  census  showed  a  population  of  93,402,151.  What 
was  the  average  governmental  expenditure  per  person  on  this 
basis  ? 


CHAPTER   VI 
FACTORS  AND  MULTIPLES 

35.  Terms.     An  integer  is  a  number  of  whole  units. 

The  factors  of  a  number  are  the  integers  which,  multiplied 
together,  produce  the  given  number.  Thus,  the  factors  of  15  are 
3  and  5  ;  the  factors  of  18  are  3  and  6,  or  2  and  9. 

A  factor  of  a  number  is  a  divisor  of  that  number. 

A  number  which  is  not  exactly  divisible  by  any  other  number 
(except  1)  is  called  a  prime  number.  Thus,  1,  3,  5,  7,  11,  and  13 
are  prime  numbers. 

Numbers  are  said  to  be  prime  to  each  other  when  they  have  no 
common  factor  except  1.  Thus,  10  and  27  are  prime  to  each  other, 
although  neither  is  a  prime  number. 

36.  Test  of  Divisibility  of  Numbers.     A  number  is  divisible  by : 

a.  Two,  if  it  ends  with  0,  2,  4,  6,  or  8.     * 

b.  Three,  if  the  sum  of  its  digits  is  divisible  by  3. 

c.  Four,  if  the  number  expressed  by  its  last  two  digits  is 
divisible  by  4. 

d.  Five,  if  it  ends  in  0  or  5. 

e.  Six,  if  it  is  divisible  by  both  2  and  3. 

/.  Eight,  if  the  number  expressed  by  its  last  three  digits  is 
divisible  by  8. 

g.    Nine,  if  the  sum  of  its  digits  is  divisible  by  9. 

h.    Ten,  if  its  right-hand  digit  is  zero. 

i.  Eleven,  if  the  difference  between  the  sums  of  the  numbers 
represented  by  the  odd  and  even  orders  of  digits  is  divisible  by  11. 
Thus,  16,280  is  divisible  by  11,  since  (8  +  6)-(0 -f- 2  +  1)  is 
divisible  by  11. 

(There  is  no  simple  method  of  testing  divisibility  by  7.) 

55 


56  FACTORS  AND  MULTIPLES 

37.  Factoring  is  the  process  of  separating  a  number  into  its 
factors.  . 

Oral  Work 

1.  Learn  the  prime  numbers  from  1  to  100  so  that  you  can 
recognize  them  at  sight. 

2.  Apply  the  tests  of  divisibility  to  the  following. 
Find  the  prime  factors  of  : 

28  160  728  478  76  720 

42  320  640  96  84  37 

72  48  386  84  90  145 

36  360  31  92  360  390 

98  280  100  81  760  625 

3.  What  numbers  between  161  and  200  are  divisible  by  9  ? 

4.  What  numbers  between  746  and  800  are  divisible  by  6  ? 

5.  Name  the  factors  of  36  which  are  not  prime  to  each  other. 

38.  Cancellation  is  the  process  of  shortening  certain  computa- 
tions involving  division  by  removing  or  canceling  equal  factors 
from  both  dividend  and  divisor. 

Example.     Divide  the  product  of  4,  9,  8,  36,  24,  and  7  by  the 

product  of  18,  2,  8,  3,  14,  and  4. 

2 

18    ;t^ 

Solution.  ^  x  ^  x  ^  x  3^  x  ^^  x  7 ^ 3^^ 

;^x;2x^x3x;^X)f 

In  all  Gomputations  involving  only  multiplication  and  division, 
cancellation  should  be  used  when  possible.  Indicate  the  multi- 
plication and  division  as  in  the  illustration  above,  then  cancel  the 
common  factors. 

Written  Work 
(Use  cancellation  when  possible.) 

24  X  36  X  15  .  4  X  37  X  16  X  5  X  60 


1 


16  X  5  X  9  *    48  X  32  X  74 

48  X  32  X  100  X  360  27  x  64  x  96  x  38 

16  X  50  X  72   *        *  19  X  16  X  9  X  2 


FACTORS  AND  MULTIPLES  57 

130x14  X  18x121  xl5  ^    144  x  32  x  63  x  7 

7  X  27  X  13  X  11        '  '         16  X  9  X  28       * 

1728x360x100x32x3  ^    21x72x160x340x27 


7. 


18  X  144  X  64  X  75  *  180  x  36  x  35 


39.  Greatest  Common  Divisor.  An  integer  that  is  a  factor  of 
two  or  more  numbers  is  called  a  common  divisor,  or  a  common 
factor  of  those  numbers. 

The  greatest  common  divisor  of  two  or  more  numbers  is  the 
greatest  factor  common  to  the  numbers.  "  Greatest  common 
divisor"  is  usually  expressed  as  g.  c.  d. 

Example.     Find  the  greatest  common  divisor  of  12,  20,  and  36. 

Solution.  12  =  2  x  2  x  3 

20  =  2  X  2  X  5 
36  =  2x2x3x3. 

The  factor  2  occurs  twice  in  all  the  numbers  and  none  of  the 
other  factors  occurs  in  all  the  numbers,  hence,  4  is  the  g.  c,  d.  of 
12,  20,  and  36. 

To  find  the  g.  c.  d.  of  two  or  more  numbers,  separate  the  numbers, 
into  prime  factors  and  find  the  product  of  the  prime  factors  common 
to  the  numbers. 

Written  Work 
Find  the  g.  c.  d.  of  : 
1.    12,  18,  24.  2.    24,  60,  72. 

3.    15,  20,  30.  4.    60,  90,  100. 

5.    84,  32,  60.  6.    60,  96,  120. 

7.    18,  32,  48.  8.    27,  36,  45. 

9.    360,  120,*  40.  10.    121,  88,  242. 

11.  Find  the  g.  c.  d.  of  8  ft.  and  12  ft. 

12.  Find  the  g.  c.  d.  of  $  48  and  f  60. 

40.  Least  Common  Multiple.  A  multiple  of  a  number  is  an 
integral  number  of  times  that  number.  Thus,  28  is  a  multiple  of 
7.     60  is  a  multiple  of  12. 


58  FACTORS  AND  MULTIPLES 

A  common  multiple  of  two  or  more  numbers  is  a  number  that  is 
a  multiple  of  each  of  them.  It  is  therefore  divisible  by  each  of 
them. 

The  least  common  multiple  of  two  or  more  numbers  is  the  least 
number  that  is  a  multiple  of  each  of  them. 

Thus,  60  is  the  least  common  multiple  of  12,  15,  and  30. 

Example.  Find  the  least  common  multiple  (1.  c.  m.)  of  18,  20, 
and  24. 

Solution.  18  =  2  x  3  x  3 

20  =  2  X  2  X  5 
24  =  2  X  2  X  2  X  3. 
1.  cm.  =  2x2x2x3x3x5  =  360. 

To  find  the  least  common  multiple  of  two  or  more  numbers, 
separate  each  number  into  its  prime  factors.  Find  the  product  of 
these  factors^  using  each  factor  the  greatest  number  of  times  it  occurs 
in  any  one  of  the  given  numbers. 

Written  Work 
P^ind  the  1.  c.  m.  of  the  following  : 

1.    12,  15.  2.  8,  12. 

3.    6,  15.  4.  7,  8,  12. 

5.    8,  9,  12,  15.  6.  24,  36,  60. 

7.    8,  12,  16.  8.  36,  24,  75. 

9.    360,  345.  10.  75,  130,  190. 

11.    425,  345,  336.  12.  360,  240,  420. 

Find  the  g.  c.  d.  and  the  1.  c.  m.  of  the  following  : 
13.    60,  80,  95.  14.    36,  75,  48. 

15.    480,  360,  120. 


CHAPTER  VII 
COMMON  FRACTIONS 

41.  Terms.     A  fraction  is  one  or  more  equal  parts  of  a  unit. 

A  common  fraction  is  usually  expressed  by  writing  one  figure 
above  and  one  below  a  short  line;  thus,  |. 

The  numerator  of  a  fraction  is  the  number  which  shows  how 
many  of  the  equal  parts  of  the  unit  are  taken.  It  is  written  above 
the  line. 

The  denominator  of  a  fraction  is  the  number  which  shows  into 
how  many  equal  parts  the  unit  is  divided.  It  is  written  below 
the  line. 

The  numerator  and  the  denominator  are  called  the  terms  of  the 
fraction.     Thus,  3  and  4  are  the  terms  of  the  fraction  |. 

A  common  fraction  may  be  either  proper  or  improper. 

A  proper  fraction  is  one  whose  numerator  is  less  than  its  de- 
nominator, as  |. 

An  improper  fraction  is  one  whose  numerator  is  equal  to  or 
greater  than  its  denominator,  as  |  or  f . 

A  mixed  number  consists  of  a  whole  number  and  a  fraction,  as  5|. 

Oral  Work 

Which  is  greater,  ^  or  |  ?     ^  or  ^^^  ?     2V  ^^  t2  ^ 
How   is   the  value   of   a   fraction   affected   by   increasing  the 
numerator,  the  denominator  remaining  the  same  ? 

Reduction  of  Fractions 

42.  Reducing  Fractions  to  Lower  Terms.  When  the  numerator 
and  the  denominator  contain  one  or  more  common  factors,  the 
fraction  may  be  reduced  t9  a  fraction  of  equivalent  value  ex- 
pressed in  lower  terms. 

59 


60  COMMON  FRACTIONS 

Thus,  \^  may  be  reduced  to  the  equivalent  fraction  J,  by  divid 
ing  both  terms  by  2.     Similarly,  J|  =  f ;   g^  =  J- 
State  a  rule  for  reducing  fractions  to  lower  terms. 

43.  Reducing  Fractions  to  Higher  Terms.  Fractions  may  be 
raised  to  equivalent  fractions  in  higher  terms,  hi/  multiplying  both 
the  numerator  and  the  denominator  hy  the  same  number. 

Example.  Express  ^  as  an  equivalent  fraction  whose  denomi- 
nator is  60. 

Solution.  The  given  denominator,  5,  must  be  multiplied  by  12  to  obtain 
the  desired  denominator,  60.  Therefore,  multiply  both  terms  of  the  fraction 
by  12,  and  obtain  the  equivalent  fraction  f  ^. 

Multiplying  or  dividing  both  terms  of  a  fraction  by  the  same 
number  does  not  change  the  value  of  the  fraction. 

44.  Reducing  Improper  Fractions  to  Mixed  Numbers.  An  im- 
proper fraction  may  be  reduced  to  a  mixed  number.  The  follow- 
ing example  shows  the  method: 

Example.     Reduce  ^^-  to  a  mixed  number. 
Solution.  19  -=-  4  =  4|. 

State  a  rule  for  changing  an  improper  fraction  to  a  mixed 
number. 

45.  Reducing  Mixed  Numbers  to  Improper  Fractions.  A  mixed 
number  may  be  reduced  to  an  improper  fraction.  The  following 
example  shows  the  method. 

Example.     Reduce  13|^  to  an  improper  fraction. 

Solution.  13  x  7  =  91.  91  +  3  =  94,  the  numerator  of  the  improper  frac- 
tion. 

The  denominator  of  the  fraction  in  the  mixed  number  is  retained  as  the 
denominator  of  the  improper  fraction. 

13f  =  -"7^. 

Oral  Work 

1.  Reduce  to  lowest  terms:   ^^,  -f^,  ^^  ^^,  ^f,  ||,  Jf,  ||. 

2.  Express  each  of  the  following  frg-ctions  with  the  denomina- 
tor 16:  f,f,i,  i|,|,f,i3. 


ADDITION  AND  SUBTRACTION  61 

3.  Express  with  the  denominator  36:   J,  |,  |,  f^"*  iV  h  h  h 

8      17 
i'    9'    2' 

4.  Reduce  to  twenty-f ourths :  |,  -^^^  h  h  h  iV'  ^* 

5.  Reduce  to  lowest  terras:  -j^g'  iV  T*6'  iV  1^2 '  ie* 

6.  Reduce  to  fiftieths:  |,  ^9_,  JL.,  la,  |,  JL. 

7.  Reduce  to  improper  fractions:  3 J,  5 J,  7|,  8|,  4f,  7|,  9^,  8|. 

8.  Reduce  the  following  fractions  to  equivalent  fractions  in 

InwPQf  tprm<i  •      9       1 6     2.0       1 8      _2  8_     21    _3  (L    2 1    _7  2_     2  4     _8_    JL8. 

lowest  termb  .   g^?  Q-g-i  35^'  Tli'  2T0'  6  3'  15 O'  T5'  i50'  36'  12'  21* 

9.  Change  the  following  fractions  as  indicated: 

f  to  an  equivalent  fraction  whose  denominator  is  20. 
1^  to  an  equivalent  fraction  whose  denominator  is  64. 
I  to  an  equivalent  fraction  whose  denominator  is  63. 
■^^  to  an  equivalent  fraction  whose  denominator  is  T2. 
■f^  to  an  equivalent  fraction  whose  denominator  is  121. 
■f^  to  an  equivalent  fraction  whose  denominator  is  84. 

10.  Change  the  following  improper  fractions  to  mixed  numbers: 

h  ¥.  ¥'  ¥'  ¥.  !4'  ^^^  ¥/.  ¥f ' !!'  W-  ^¥- 

11.  Change   the   following   mixed  numbers  to  equivalent  im 
proper  fractions:  3|,  6f  8^,  4|,  8if,  10J|,  14^^  12^^,  18^3^,  9^^. 

12.  When  we  reduce  -^^  ^^  h  ^^  we  increase  or  decrease  the 
size  of  the  fractional  unit  ?  Do  we  increase  or  decrease  the  num- 
ber of  fractional  units  ? 

13.  Which  fraction  is  the  greatest,  |^,  J,  |,  -^|  ? 

Addition  and  Subtraction  of  Fractions 

46.  Finding  the  Least  Common  Denominator.  Only  like  quan- 
tities can  be  added  or  subtracted.  It  is  not  possible  to  add  or 
subtract  4  lb.  and  2  oz.  or  J  and  J  until  they  are  reduced  to  the 
same  denomination. 

The  common  denominator  should  be  the  smallest  number  which 
will  exactly  contain  all  of  the  denominators.  It  may  usually  be 
found  by  inspection. 

Any  number  which  contains  all  of  the  factors  of  another  number 


62  COMMON  FRACTIONS 

will  also  contain  that  number.  Thus,  24  contains  all  of  the  factors 
of  12,  and  it  therefore  contains  12. 

The  common  denominator  must,  therefore,  contain  all  of  the 
factors  of  the  denominators. 

Hence,  to  find  the  least  common  denominator  of  two  or  more 
fractions,  find  the  prime  factors  of  the  denominators  ;  multiply  the 
different  prime  factors^  using  each  factor  the  greatest  number  of 
times  it  is  contained  in  any  one  denominator. 

Example.  What  is  the  least  common  denominator  of  fractions 
with  the  denominators  8,  9,  and  12  ? 

Solution.  8  =  2x2x2. 

9  =  3x3. 
12  =  2  X  2  X  3. 
1.  c.  m.  of  denominators  =  2x2x2x3x3. 

47.  Reducing  Fractions  to  a  Common  Denominator.  After  the 
least  common  denominator  has  been  found,  the  fractions  may  be 
reduced  to  this  denominator. 

Example.     Reduce  |,  |^,  and  |  to  a  common  denominator. 
Solution.     The  common  denominator  is  30. 

t  =  M- 
State   the  process  of  reducing  fractions  to  a  common  denom- 
inator. 

Written  Work 

Reduce  the  fractions  in  each  example  to  fractions  having  the 
least  common  denominator : 

1.    \  and  \.                  2.    \  and  \.  3.    \  and  |. 

4.    1,  i,  and  iV-           5.    |,  -jV,  sV-  6.    |,  |,  ^. 

7      J.      2        5  R      jr_      9      la    A    _5  Q    _3^     11    ^a_    12 

''     7'  TT'  IS"-  **•      12'  ^2'  "&6'   9'   li-         ^-    2(7'   J6'  19'   55- 

48.  Rule  for  Addition  of  Fractions. 

Reduce  the  fractions  to  a  common  denominator.  Add  the  numerators 
to  form  the  numerator  of  the  sum.  The  common  denominator  is  the  cZe- 
nominator  of  the  sum.     Reduce  the  result  to  the  simplest  form. 


ADDITION  AND  SUBTRACTION  63 

Proper  fractions  should  be  reduced  to  their  lowest  terms. 
Improper  fractions  should  be  changed  to  mixed  numbers. 

Examples.     1.    Add  |  and  |. 

Solution.     The  least  common  multiple  of  the  denominators  is  12. 


T%   +  T%  =  ii  =  ItV 

2.    Add  f ,  I ,  and  ^3^. 

Solution.     The  least  common  multiple  of  the  denominators  is  60. 

5  _   50 

6  —   5^- 

49.  Rule  for  Subtraction  of  Fractions. 

The  process  is  the  same  as  for  Addition  of  Fractions  except  that  the 
numerators  are  subtracted  instead  of  added  after  the  fractions  have  been 
reduced  to  a  common  denominator. 

Oral  Work 
State  the  sum,  then  the  difference  of  the  following: 

1.    1   \.            2.    i  \.            3.    i,  \.            4.    i,  1.            5.  i,  1. 

6.    ^,J.            7.     \,\.            8.    1   ,V          9-    l-f          10.  f,^. 

11.     1,  J.          12.    |,  |.          13.    -f,  i.          14.    |,  |.          15.  f,  f . 

Note.  The  Short  Methods  for  the  Addition  and  Subtraction  of  Fractions, 
explained  on  pages  69-71,  may  he  studied  at  this  time. 

50.  Rule  for  Addition  of  Mixed  Numbers. 
Add  the  fractions. 

If  the  sum  is  an  improper  fraction,  reduce  it  to  a  mixed  number. 
Add  the  sum  of  the  fractions  to  the  sum  of  the  integers. 

Example.     Add  3|  and  4|. 

Solution.  |  +  |  =  i/  =  If. 

3^4  =  7. 

7  +  If  -=  8^ 


64  COMMON  FRACTIONS 


Written  Work 

Find  the  sums : 

1.   4^+3^. 

2.    2i  +  5f 

3.    7i  +  5f. 

4.    17^  +  18f. 

5.    2751  +  78^. 

6.   3J  +  51. 

7.    9iV  +  17f. 

8.    8J+4f  +  8Jj. 

9.    23J  +  16j^ 

+  7f. 

10.    18|  +  42j-V  +  37|. 

51.    Rule  for  Subtraction  of  Mixed  Numbers. 

If  the  fraction  of  the  minuend  is  larger  than  that  of  the  subtra- 
hend, the  above  rule  for  addition  can  be  easily  changed  to  apply 
to  subtraction. 

Example.     Subtract  4|  from  Tf. 
Solution.  |  —  §  =  |3, 

7  -  4  ==  3. 

Result  3|f . 

If  the  fraction  of  the  minuend  is  smaller  than  that  of  the  subtra- 
hend, we  may  proceed  as  follows : 

Example.     Subtract  4|  from  9J. 

Solution,  f  cannot  be  subtracted  from  \,  but  9^  may  be  regarded  as  8f . 
I  -  t  =  tV     Therefore,  9^  -  4|  =  4^^. 


Add  as  indicated  : 

Written  Work 

1-  f+f- 

4-  -A  +  A- 

7.    3|  +  f 

5-  f  +  A  +  A-               6.  if  +  A  +  H 
8.  12^e+T'F-                  9-  13f  +  22T9j. 

Subtract  as  indicated : 

10.    f-3\.           11. 

14.  ^-^.    IS. 

-A- 

12.  2^5-^.         13.  4|-f 
16.  5^-2|. 

Add  upward  and  across : 

17. 

18. 

i  +  i+    I 
f  +  f  +  A 

!  +  *+  f 

i+A+  1 

A+    1+2^ 

■i+  *+  f 
?  +  y  +  ? 

MULTIPLICATION  AND  DIVISION  65 

19.    Add  upward  ,•  subtract  across : 

l^-^ 

181 -7f 
151 -7» 

?         —     ? 

Multiplication  and  Division  of  Fractions 

52.   Rule  for  Multiplication  of  Fractions. 

Multiply  the  numerators  to  form  the  numerator  of  the  product.  Multi- 
ply the  denominators  to  form  the  denominator  of  the  product.  Reduce 
the  product  to  its  simplest  form.  ^ 

Note.     The  word  "of"  placed  between  fractions  indicates  multiplication. 

Mixed  numbers  should  be  changed  to  improper  fractions  before 
multiplying. 

Example.     8  x  6|  x  f  x  3f  =  ? 

Solution.  Reducing  mixed  numbers  to  improper  fractions :  f  x  ^  x  | 
X  ^-  =  ? 

2       9 

^      ^7     2      19 

1      1 

Multiplying  the  resulting  numerators :  2  x  9  x  2  x  19  =684,  the  numerator  of 
the  product. 

Multiplying  the  resulting  denominators :  1x1x1x5  =  5,  the  denominator 
of  the  product. 

Changing  to  a  mixed  number :  ^^  =  136^,  the  product. 

Written  Work 
Perform  the  following  multiplications: 
1.    fxf  2.    fxf  3.    fxf 

4.    ix/^.  S-    |X|-  6.    3Jx4|. 

7.    fx|.  8.    f0f|xj.  9.    fxfoff. 

10.   ^s^-xfxfx^.   11.    5|x3ix4f.       12.   |x4xjx^. 


66  COMMON  FRACTIONS 

53.   Rule  for  Division  of  Fractions. 

Invert  the  divisor j  and  multiply  the  fractions,  using  cancellation  when 
possible. 

Examples,     i.  t-f  =  f  x|  =  -if 

2     -8  ^  ^  =  ^  X  4  =  J-Q.  —  11 

3.    8-i-^4=? 


13      3 

Solution. 

2 
Writjen  Work 

1-  1^1- 

2.    |-  X  |. 

3. 

foffxl 

4.   5i  +  4|. 

5.  7i^3f 

6. 

f+l. 

'•   l-f        • 

8.  3i  +  5f. 

9. 

1  of  f 

10.    9|  xl2f^3f 

11.  |off^^i|., 

12. 

I+I-. 

13.   4f-3i  +  5i. 

14.  17|x6J^4t^. 
Review  Exercises 

15. 

loff^f 

off 


1.  Multiply  each  of  the  fractions  in  the  column  at  the  left  by 
each  of  the  fractions  at  the  top.  Enter  the  products  in  the  spaces 
formed  by  the  horizontal  and  vertical  lines.  (For  example,  the 
space  marked  "  X  "  is  to  contain  the  product  of  f  and  J.) 


Multiply 

1 

1 

1 

1 

5 
6 

H 

6 

8 

X 

7 
8 

MULTIPLICATION  AND  DIVISION 


G7 


2.  In  the  following  form  divide  each  of  the  fractions  in  the 
column  at  the  left  by  the  fractions  in  the  upper  row.  Rule  a 
blank  similar  to  the  form  given  and  record  the  quotients  in  the 
proper  spaces. 


1 

1 

5 

6 

8 
3 

3 
4 

2 
5 

4 

'    9 

5 
4 

3 

8 

5 
12 

8 
9 

5 
6 

Miscellaneous  Problems 

1.  If  ^  of  a  number  is  5,  what  is  the  number  ? 

2.  If  1^  of  a  number  is  12,  what  is  the  number  ? 

3.  If  ^  of  a  number  is  20,  what  is  the  number  ? 

4.  If  I  of  f  of  a  number  is  15,  what  is  the  number? 

5.  After  spending  ^  of  his  monthly  salary  for  board  and  room, 
and  ^  of  it  for  clothes,  a  man  has  $  63  left.     What  is  his  salary  ? 

6.  If  5  yards  of  cloth  cost  47J  ^,  what  will  1  yard  cost  at  the 
same  rate  ? 


68  COMMON  FRACTIONS 

7.  A  train  runs  f  of  a  mile  in  |  of  a  minute.  What  is  the  rate 
per  hour  ? 

8.  Which  will  give  the  larger  result,  multiplying  or  dividing 
an  integer  by  a  proper  fraction  ?  Multiplying  or  dividing  by  an 
improper  fraction  ? 

9.  If  you  are  told  the  amount  of  a  man's  wages  and  the  frac- 
tional part  of  his  wages  which  he  spent,  how  can  you  find  the 
fractional  part  which  he  saved  ? 

10.  State  two  ways  of  finding  the  amount  saved,  and  state 
which  you  think  is  the  easier. 

11.  If  you  were  told  what  |  of  |^  of  a  number  is,  how  could  you 
find  the  number  ? 

12.  A  man  owned  f  of  a  farm  and  sold  ^  of  what  he  owned.  If 
he  received  $  3000  for  the  land  sold,  what  was  the  value  of  the 
entire  farm  at  the  same  rate  ? 

13.  A  mechanic  works  8  hours  a  day.  Two  and  one  half  hours 
are  spent  at  a  bench  and  the  remainder  at  a  machine.  What 
fractional  part  of  the  day  is  spent  at  a  machine  ? 

14.  In  a  certain  family  ^  of  the  yearly  income  is  spent  for  rent, 
^  for  clothes,  ^  for  food,  and  J  of  the  remainder  for  travel.  If 
the  yearly  income  is  $  3000,  how  much  is  spent  for  travel  ? 

15.  A  man  sold  |  of  an  acre  of  land  for  $  76.  At  that  rate 
what  is  his  farm  of  120  acres  worth? 

16.  ^  of  the  number  of  students  in  a  high  school  are  girls.  The 
number  of  boys  is  120.     How  many  students  are  there  in  the  school? 

17.  Mr.  Jones  bought  some  land  and  sold  it  so  as  to  realize  J 
more  than  the  cost.  If  the  selling  price  was  $  360,  what  did  he 
pay  for  the  land  ? 

18.  Mr.  Williams  sold  some  goods  for  J  less  than  the  cost.  If 
he  received  $  70  for  the  goods,  what  was  the  co/^t  ? 

19.  In  making  up  a  certain  cake  recipe  for  6  people,  IJ  cups 
of  sugar  and  f  of  a  cup  of  butter  are  used.  How  much  sugar  and 
butter  should  be  used  in  making  up  the  recipe  for  4  people  ? 

20.  A  boy  works  3 J  days  at  the  rate  of  $  6.50  a  week  of  6  days. 
How  much  does  he  earn  ? 


SHORT  METHODS  69 

21.  Find  the  total  cost  of  8|  yards  of  ribbon  at  28  cents  per 
yard,  3|  yards  of  insertion  at  12^  cents  per  yard,  and  5J  yards  of 
silk  at  ^  1.35  per  yard. 

22.  A  dealer  bought  oranges  at  the  rate  of  4  for  10  cents  and 
sold  them  at  the  rate  of  3  for  10  cents.  How  much  did  he  gain 
on  each  orange  ? 

23.  Mr.  Rankin  owned  |  of  a  store  and  sold  |  of  his  share  to 
Mr.  Johnson  for  $  3600.     At  this  rate  what  was  the  store  worth  ? 

24.  If  a  man  drives  his  automobile  18  miles  in  |  of  an  hour, 
how  long  would  he  require,  at  the  same  rate,  to  travel  60  miles  ? 

25.  When  I  of  a  yard  of  cloth  costs  $  1.80,  what  is  the  price  of 
|-  of  a  yard  ? 

26.  A  girl  grew  1^  inches  during  one  year  and  |  of  an  inch 
during  the  next  year.  How  much  more  did  she  grow  during  the 
first  year  than  during  the  second  ? 

27.  The  entire  length  of  a  skirt  is  to  be  26|  inches,  and  the 
ruffle  at  the  bottom  is  to  be  3^  inches  wide.  What  will  be  the 
length  of  the  skirt  above  the  ruffle  ? 

28.  The  record  for  the  hundred  yard  dash  is  9|  seconds.  A 
boy  can  run  the  distance  in  11-|  seconds.  What  is  the  difference 
between  his  time  and  the  record  time  ? 

29.  A  farmer  raised  296^  bushels  of  wheat  on  15J  acres. 
What  was  the  average  yield  per  acre  ? 

30.  Three  and  one  half  bushels  of  seed  were  sown  and  the  yield 
was  21-|  bushels.     What  was  the  average  yield  per  bushel  of  seed  ? 

Shqrt  Methods  Involving  Fractions 

64.    To  add  fractions  when  the  numerators  are  the  same. 

Add  the  denominators  and  multiply  this  sum  by  the  commoii  numerator 
to  obtain  the  numerator  of  the  result.  Multiply  the  denominators  to  obtain 
the  denominator  of  the  result.     Reduce  to  simplest  form. 

Examples.     1.  Add  \  and  |. 

Solution.    3  -f-  7  =  10,  the  numerator  of  the  result. 

3  X  7  =  21,  the  denominator  of  the  result. 
Hence,  ^  +  j  =  ^$. 


70  COMMON  FRA.CTIONS 

2.    Add  I  and  |. 

Solution.     5  +  9  =  14.     14  x  2  =  28,  the  numerator  of  the  result. 

5  X  9  =  45,  the  denominator  of  the  result. 

Hence,  i  +  l=  If. 


Oral  Work 

Add  as  indicated : 

1-     i  +  i-                   2- 

Ki 

3. 

i+h 

4. 

i  +  l\ 

5.    j  +  i.                  6. 

iV  +  f 

7. 

h  +  l\- 

8. 

f+t^ 

9.    J+f                10. 

f  +  l- 

11. 

l\  +  f 

12. 

l  +  f 

13.    I+^V              "• 

I  +  tV 

55.  To  subtract  fractions  when  the  numerators  are  the  same. 

Subtract  the  denoininators  and  multiply  this  difference  by  the  common 
numerator  to  form  the  numerator  of  the  result.  Multiply  the  denominators 
to  form  the  denominator  of  the  result.     Reduce  to  simplest  form. 

Example.     Subtract  -|  from  |. 

Solution.     5  —  3  =  2.    2x2=4,  the  numerator  of  the  result. 
5  X  3  =  15,  the  denominator  of  the  result. 
Hence,  |  -  1  =  xV 

Oral  Work 
Perform  the  following  subtractions : 

*•  l-iV  5-  f-A-  6-  i-~h- 

56.  To  add  two  fractions  by  "  cross  multiplication." 

Multiply  the  numerator  of  each  fraction  by  the  denominator  of  the  othe> 
fraction.  Add  these  products  to  form  the  nuynerator.  Multiply  the  de- 
nominators to  form  the  denominator.     Reduce  to  lowest  terms. 

Example.     Add  |  and  |. 

Solution.  2x4  =  8. 

3x3  =  9. 

9  +  8  =  17,  the  numerator. 

3  X  4  =  12,  the  denominator. 
Hence,  f  +  |  =  \h  H  =  1^- 


SHORT  METHODS  71 


Oral  Work 

Add  as  indicated : 

1-  f+f 

2.    f  +  f 

3.   J  +  |. 

*•    fff  +  T^- 

5-    l  +  f 

6-   l  +  f 

'•    A  +  l-     . 

8.    f +iV 

9-    f  +  tV- 

57.    To  subtract  fractions  by  "  cross  multiplication." 

Multiply  the  numerator  of  each  fraction  by  the  denominator  of  the  othet 
fraction.  Subtract  these  products  to  form  the  numerator.  Multiply  the 
denominators  to  form  the  denominator.     Heduce  to  lowest  terms. 

Example.     Subtract  J  from  |^. 

Solution.  5  x  3  =  15. 

6  X  2  =  12. 
15  —  12  =  3,  the  numerator. 
6  X  3  =  18,  the  denominator. 
Hence,  i  -  f  =  t\,  t\  =  i- 

Written  Work 
Subtract  as  indicated  : 


1. 


4  _  1  2-8 -3.  3      4 3_  4      7 I_ 

Y        3-  '^-     11         6-  **•    1^        TO-  *•     g         11 


58.    To  find  the  approximate  product  of  mixed  numbers. 

Multiply  the  integers.     Multiply  each  integer  by  the  other  fraction  to  the 
nearest  unit.     Add  these  three  products. 

Example.     Multiply  13|  by  6|. 

Solution.  13| 

6| 

13  X  6  =  78 
^  of    6  =    3 

f  of  13  =_£  (to  the  nearest  unit). 
90 

Written  Work 
Find  approximate  products  : 
1.    431  2.  891  3.   761  4.  152  5.   ggi 

^^  ^  82|  40f  47J 


72 


COMMON  FRACTIONS 


6.-  17f 

46| 


7.  13f 

16i 


8.   79| 
63i 


9.  38| 
71i 


10.  73| 

96| 


59.    To  find  the  product  of  any  two  numbers  ending  in  J. 
(a)  When  the  sum  of  the  integers  is  an  even  number. 
To  the  product  of  the  integers,  add  one  half  of  their  sum  and  annex  \  t6 
the  result. 


Example. 

Multiply  391  by  3J. 

Solution. 

39i 

n 

39  X  3  =  117 

i  the  sum  of  39  and  3  =    21 

138|  Result, 

Written  Work 

Multiply : 

1.    44J 

2.  181        3.  381          4.  751 

641 

121              141                351 

5.  29J 

331 


6.  81| 

75J 


(6)  When  the  sum  of  the  integers  is  an  odd  number. 
To  the  product  of  the  integers,  add  the  result  obtained  by  taking  half  of 
one  less  than  their  sum.     To  this  result  annex  4. 


Example. 

Multiply  39 

'i  by  61 

Solution. 

39^ 

Ji 
234 

22 

256f 

Written  Work 

Multiply: 

1.    73J 

2.   571 

3.    92J 

4.   85J 

5.   98J 

42J 

24J 

47J 

58J 

in 

6.    29* 

7.   83J 

8.    76J 

9.  4ej 

10.   98^ 

361 

96J 

19J 

46J 

231 

11.    481 

12.    951 

13.    73J 

14.   47J 

15.    271 

72^ 

81i 

71J 

33| 

^H 

CHAPTER  VIII 
DECIMAL  FRACTIONS 

60.    Comparison  of  Common  and  Decimal  Fractions. 

The  denominator  of  a  common  fraction  may  be  any  number,  and 
it  is  always  expressed. 

The  denominator  of  a  decimal  fraction  is  always  some  power  of 
10,  and  the  power  is  indicated  by  the  number  of  figures  to  the 
right  of  the  decimal  point. 

7 


.7  = 

< 
10* 

.07  = 

7 
100 

007  = 

7 

Thus,        .7  =  ;^.  .0007 

.423  = 
.027  = 


10000 
423 

1000* 

27 


1000  1000 

61.    Reading  and  Writing  Decimals. 

The  names  of   the  various   decimal   orders  are  stated   in   the 
following  table  : 


CO 

4^ 

M 

T3 

T3 
C 

2 

to 

(0 

o 

■o 

C 

3 

•6 

x: 

(0 

SI 

0> 

■a 

2 

3 

O 

1- 

<•< 

c 

1 

c 

c 

O 

c. 

C 

^ 

c 

a> 

3 

f 

0) 

3 

•~ 

a> 

h- 

I 

1- 

1- 

I 

s 

1- 

1 

2 

3 

4 

5 

6 

7 

The  names  of  the  various  orders  should  be  learned.  You 
should  know  that  the  name  of  the  third  decimal  order  is  thou- 
sandths i  that  of  the  fifth  is  hundred-thousandths  ;  that  of  the 
second  is  hundredths,  etc. 

73 


74  DECIMAL  FRACTIONS 

To  read  a  decimal  fraction^  read  the  number  as  if  it  were  an  integer 
and  then  state  the  name  of  the  last  decimal  order  which  a  digit  of  the 
number  occupies. 

Pronounce  the  word  "and"  at  the  decimal  point  and  omit  it 
elsewhere,  except  in  reading  complex  decimals  as  noted  below  : 
.045  is  read  forty-five  thousandths. 
.505  is  read  five  hundred  five  thousandths. 
500.005  is  read  five  hundred  and  five  thousandths. 
.4206  is  read  four  thousand  two  hundred  six  ten-thousandths. 
.0|  is  read  two  thirds  of  a  tenth. 
2.0|  is  read  two  and  two  thirds  of  a  tenth. 
.2|  is  read  two  and  two  thirds  tenths  (a  complex  decimal). 
Read : 

2.    .1764.  3.    2.04. 

5.    400.004.  6.    .00|. 

8.    .000562.  9.    64.3. 

11.    .003726.  12.    542.54. 

14.    .000241.  15.    7.00707. 

Write  decimally  : 

1.  Seven  tenths ;  forty-two  thousandths ;  five  hundred  four 
thousandths. 

2.  Four  hundred  and  three  thousandths;  eight  hundred  two 
ten-thousandths. 

3.  Three  fourths  of  a  tenth  ;  two  and  one  seventh  tenths. 

4.  Twenty-four  ten-thousandths  ;  five  millionths  ;  seventeen 
hundred-thousandths  ;  two  hundred  and  three  hundredths. 

5.  Five  hundred  seventeen  millionths  ;  sixteen  ten-thousandths; 
eighteen  hundred  and  fifteen  ten-thousandths. 

6.  Five  thousand  four  hundred-millionths  ;  eighteen  and  four 
thousandths. 

62.    Addition  of  Decimal  Fractions. 

Place  the  decimals  so  that  the  decimal  points  fall  vertically.  Add  as 
with  integers.  Place  the  decimal  point  of  the  sum  directly  below  those  in 
the  numbers  added. 


1. 

.043. 

4. 

500.17. 

7. 

214.0014. 

10. 

14.003. 

13. 

3005.016. 

DECIMAL  FRACTIONS  75 

Example.     Find  the  sum  of  4.023,  .507,  2.003,  and  1.125. 
Solution.  4.023 

.507 

2.003 

1.125 

7.658 

Written  Work 

1.  Add   2569.327,    1462.978,     47.9634,    2693.072,    and    .019. 

2.  Add  27.9548,  91.0005,  37.427,  and  27563.974. 

3.  Add  2752.9374,  .0003,  23.247,  and  259.6347. 

Change  the  following  common  fractions  to  decimal  fractions, 
and  add : 

24     372     19    254 
'    100'  1000'  10'  loo' 

3  24      675     170 


1000'  10000'   10  '  10000 


6. 


100        1000' 

10000'  1000 

Copy,  find  the  totals  required. 

and  check  : 

$  324.80 

1  3764.20 

$7436.08 

? 

17.04 

762.83 

427.36 

? 

9320.87 

9402.03 

92.18 

? 

473.26 

1.18 

4724.63 

? 

791.14 

13420.03  • 

924.56 

? 

? 

? 

? 

? 

63.    Subtraction  of  Decimal  Fractions. 

Place  the  decimals  so  that  the  points  fall  vertically.  Subtract  as  with 
integers,  then  place  the  decimal  point  in  the  remainder  immediately  below 
the  decimal  points  above. 

Example.     Subtract  23.213  from  34.047. 

Solution.  *  34.047 

23.213 
10.834 


76  DECIMAL  FRACTIONS 

Subtract  as  indicated.     Check  the  results. 
1.    394.237-1.027.       2.    .47 -.0003.       3.    .394237 -.15. 

4.  7763.421-28.796.  5.    87.5932      2.3579. 

Change  to  decimal  fractions  and  subtract : 

6     i^-^           7     ^^^43      235  8732     236547 

1000      100*            *      100        1000*  *      10       100000 ' 

9.    The  sum  of  two  numbers  is  342.086.  One  of  the  numbers 
is  206.78.     What  is  the  other  number  ? 

10.  A  man  deposited  $5764.80  in  a  bank.  He  later  drew  out 
13780.92  and  then  he  deposited  14814.60.  How  much  had  he 
then? 

64.   Multiplication  of  Decimal  Fractions. 

Multiply  as  with  integers.  From  the  right  of  the  product,  point  off  as 
many  places  as  the  sum  of  the  number  of  decimal  places  in  the  multipli- 
cand and  the  multiplier. 

Examples*.     1.     Multiply  4.625  by  .05. 

Solution.  4.625 

^ 

.23125 

2.  Multiply  .00362  by  .06. 

Solution.  .00362 

.0Q_ 

.0002172 

Written  Work 
Multiply  as  indicated.     Check  the  results. 
1.    25.763  X  .1463.  2.    75.46  x  .03. 

3.    .2462  X. 347.  4.    .083  x  .0462. 

5.  78.23  X  .000007.  6.    17.13  x  .042. 

7.    570.04  x  .00326.  8.    1374.26  x  .055. 

9.    $9037.28  X  .035.  10.    1473.54  x  .335. 

11.  Find  the  cost  of  46  lots  at  an  average  cost  of  1847.60. 

12.  Find  the  cost  of  143  barrels  of  apples  at  an  average  price  of 
83.64  per  barrel. 


DECIMAL  FRACTIONS  77 

65.    Division  of  Decimal  Fractions. 
a.    When  the  divisor  is  an  integer. 

Examples.     1.    .12-5-4  =  .03;  just  as  112^4  =  |3. 

2.  .426  ^3  =  .142;  just  as  1426  ^  3  =  1142. 

In  making  the  division  the  decimal  point  should  be  written  in 
the  quotient  when  it  is  reached  in  the  dividend. 

3.  Divide  157.25  by  37. 
Solution.  4.25 

37)157.25 
148 
9.2 
7.4 
1.85 
1.85 

h.    When  the  divisor  is  not  an  integer. 

Multiple/  both  dividend  and  divisor  hy  the  least  power  of  ten  that 
will  make  the  divisor  an  integer.     Divide  as  in  case  a. 

Example.     Divide  .028  by  .4. 

Solution.  First  multiply  both  dividend  and  divisor  by  10,  to  make  the 
divisor  an  integer.  Then  divide  the  resulting  dividend,  .28,  by  4.  The  result 
is  .07. 

Similarly,  .0456  --  .03  =  4.56  -^  3  =  1.52. 

Similarly,  5.64  -  .0004  =  56400  ^  4  =  14100. 

If  there  is  a  remainder  after  all  of  the  decimal  places  in  the 
dividend  have  been  used,  zeros  may  be  annexed  to  the  dividend 
and  the  division  may  be  carried  as  far  as  is  desired. 

Oral  Work 

1.    .08  by  .4.                  2.    .014  by  .2.  3.  .364  by  .04. 

4.    3300  by  .11.             5.    8.48  by  .008.  6.  .220  by  .0011. 

7.    1  by  .01.                   8.    .10  by  .1.  9.  .018  by  18. 

10.    .0001  by  .00001.     11.    .042  by  2.1.  12.  1.1  by  .011. 


78  DECIMAL  FRACTIONS 

Written  Work 

1.  268632^36.9.  2.  26863.2^36.9. 

3.  26863.2-^369.  4.  2686.32-^-36.?. 

5.  26.8632^36.9.  6.  2686.32-- .369. 

7.  26.8632- .369.  8.  26.8632 -- .0369. 

9.  2.68632 -.369.  10.  2.68632^-3.69. 

11.  2. 68632 -J- 36.9.  12.  2.68632-369. 

13.  .268632-^369.  14.  2.68632-^3690. 

15.  293.45-^14.24.      '  16.  2.734-1.32. 

17.  .73469 -f- 127.9638.  18.  762.397^36947.28. 

19.  .1479376^-293.4798.  20.  .0097^12.34692. 

21.  The  multiplier  is  .045,  the  product  is  .01665.  What  is  the 
multiplicand  ? 

22.  At  f  .24  per  dozen,  how  many  eggs  can  be  bought  for 
14.08? 

23.  If  a  man's  annual  income  is  $5420  and  his  annual  expenses 
are  $4262,  what  are  his  average  weekly  savings  ? 

24.  What  number  is  ^  as  large  as  .0427  ? 

25.  What  number  divided  by  4.28  gives  a  quotient  of  .07  and  a 
remainder  of  .04  ? 

26.  In  a  certain  factory  30  men  are  employed  at  f  2.15  per  day, 
10  men  at  13.60  per  day,  28  men  at  $2.90  a  day,  and  12  men  at 
$1.80  a  day.     Find  the  average  daily  wage. 

27.  Using  the  current  market  price  find  the  cost  of  the  follow- 
ing :  1  pk.  of  apples,  J  bu.  of  sweet  potatoes,  |  lb.  of  tea,  6  bars 
of  laundry  soap,  IJ  lb.  porterhouse  steak. 

28.  A  train  ran  at  the  rate  of  .87  mile  a  minute.  At  this  rate 
how  many  miles  would  it  travel  in  3 J  minutes  ?  In  10  minutes  ? 
In  1  hour  ? 

29.  An  automobile  traveled  72.25  miles  in  2 J  hours.  What 
was  the  average  rate  of  speed  per  hour  ? 


DECIMAL  FRACTIONS  79 

66.    Changing  Decimal  Fractions  to  Equivalent  Common  Fractions. 

Omit  the  decimal  point;  write  for  the   denominator  1  with   as  many 
zeros  annexed  as  there  are  places  in  the  decimal.     Reduce  to  longest  terms. 

Examples.     1.     Change  .75  to  a  common  fraction. 
Solution.  .75  =  ^-^  =  f. 

2.    Change  .00864  to  a  common  fraction. 
Solution.  .00864  = 

Written  Work 

Change  the  following  decimals  to  equivalent  common  fractions 
and  reduce  to  lowest  terms  : 


1. 

.48. 

2.  .095. 

3.  .3705. 

4.  .0012. 

5    8.6425. 

6. 

.125. 

7.  .9825. 

8.  .625. 

9.  .1875. 

10    .0015. 

11. 

.06  J. 

12.  .0021. 

13.  .37f 

14.  .333. 

15.   .012f 

16. 

.006|. 

17.  .00625. 

18.  .0086. 

19.   .008 J. 

20.   .0093-L 

21. 

.OOIJ. 

67.   Changing  Common  Fractions  to  Equivalent  Decimal  Fractions. 

Since  a  common  fraction  may  be  regarded  as  an  indicated  di- 
vision, the  reduction  may  be  made  by  the  methods  of  division 
previously  explained. 

Example.     Change  ^  to  a  decimal  fraction. 

Solution.     |  =  ^  of  4.     Place  a  decimal  point  to  the  right  of  the  4,  annex 

.8 


zeros,  and  divide. 

5)4.0 

.875 

Similarly,  |  =  1  of  7. 

8)7.000 

.0053+ 

Similarly,  ^^  =  ^\^  of  2. 

375)2.000 

1.875 

.1250 

.1125 

125 

It  is  usually  not  necessary  to  carry  the  division  more  than  three 
or  four  places. 

For  example,  |  may  be  expressed  decimally  as  .142|^  or  as  -.1429". 


80 


DECIMAL  FRACTIONS 


Written  Work 

Considering  the  figures  in  the  top  row  as  numerators,  and  those 
at  the  left  as  denominators,  change  the  common  fractions  thus 
formed  to  decimals,  entering  the  results  in  the  proper  places. 
Carry  the  results  to  three  decimal  places. 

Prepare  the  work  on  a  carefully  ruled  form. 

68.  Approximate  Results.  For  most  practical  purposes  it  is  un- 
necessary to  carry  a  result  to  more  than  three  decimal  places. 
Thus,  $25.86347  is  stated  with  sufficient  accuracy  as  125.86. 

In  finding  approximate  decimal  fractious,  follow  these  direc- 
tions. 

Carry  the  division  at  least  one  more  place  than  the  number  of  digits 
desired  in  the  result.  If  the  digit  at  the  right  of  the  last  place  de- 
sired in  the  result  is  less  than  5,  drop  it;  if  it  is  5  or  larger  than  5, 
increase  the  preceding  digit  by  1. 


Denominators 

Ntjmbratobs 

3 

7 

6 

26 

47 

126 

79 

814 

1216 

18 

27 

94 

38 

. 

172 

9 

66 

213 

793 

2361 

43 

109 

DECIMAL  FRACTIONS 


81 


Written  Work 

The  following  table  gives  the  land  area,  in  acres,  of  the  differ- 
ent geographical  sections  of  the  United  States,  and  the  number 
of  acres  in  each  section  devoted  to  farming. 

Prepare  a  ruled  form  similar  to  the  model. 

Find  what  decimal  part  of  the  land  area  of  each  section,  and  of 
the  United  States,  is  improved  farm  land.  (Approximate  results 
to  the  nearest  thousandth.) 

Also  find  the  total  land  area  of  the  United  States,  the  total  area 
of  the  improved  land,  and  the  fraction  of  the  total  area  which  is 
improved. 

Arrange  the  different  sections  on  the  blank  in  the  order  of  their 
rank,  placing  the  section  with  the  largest  fraction  of  improved 
farm  land  at  the  top  of  the  blank. 


Total  Land 
Area 

Improved  Farm  Land 

Acres 

Acres 

Decimal  Fraction 
of  Total 

New  England 

Middle  Atlantic 

East  North  Central    .... 
West  North  Central  .... 

South  Atlantic 

East  South  Central    .... 
West  South  Central  .... 

Mountain 

Pacific 

39,664,640 
64,000,000 
157,160,960 
326,914,560 
172,205,440 
114,885,760 
275,037,440 
549,840,000 
203,580,800 

7,254,904 
29,320,894 
88,947,228 
164,284,862 
48,479,733 
43,946,846 
58,264,273 
15,915,002 
22,038,008 

United  States 

Oral  Work 

The  following  table  shows  : 

The  value  of  the  butter  sold  in  each  section  of  the  United  States 
in  a  recent  year. 

The  fractions  which  these  values  were  of  the  total  production  of 
butter  in  each  section. 


82  DECIMAL  FRACTIONS 

Value  of  Butter  Produced  in  United  States 


Section 

Value  of 

Fraction  of  Total 

Value  of  Total 

Butter   Sold 

Product  Sold 

Production 

New  England    .... 

$  8,533,864 

.725 

a 

Middle  Atlantic     . 

15,229,862 

.655 

East  North  Central 

31,855,809 

.585 

West  North  Central 

20,333,127 

.438 

South  Atlantic  .     . 

7,622,916 

.275 

East  South  Central 

4,842,959 

.167 

West  South  Central 

5,381,690 

.19 

2,166,918 
4,410,978 

.422 

Pacific 

.572 

1.  By  referring  to  the  table  we  find  that  .725  of  the  butter 
produced  in  New  England  was  sold.  How  many  tenths  of  the 
butter  made  in  New  England  was  sold  ? 

2.  If  f  4,410,978  is  about  fifty-seven  hundredths  of  the  value 
of  all  the  butter  made  in  the  Pacific  States  in  a  year,  how 
would  you  find  the  total  value  of  the  butter  production  in  this 
section  ? 

Note.  When  in  doubt  whether  the  solution  of  a  given  problem  requires  multi- 
plication or  division,  replace  the  given  numbers  by  smaller  numbers.  Reread  the 
problem  v\rith  these  small  numbers,  and  decide  upon  the  process. 

3.  Will  the  numbers  to  be  recorded  in  the  last  column  of  the 
preceding  blank  be  larger  or  smaller  than  those  in  the  first 
column  ? 


Written  Work 

Rule  a  blank  similar  to  the  one  above. 

Find  the  total  value  of  the  butter  produced  in  each  section. 
(Approximate  results  to  the  nearest  dollar.) 

Enter  the  sections  on  the  blank  in  the  order  of  their  rank  as 
butter  producers. 


DECIMAL  FRACTIONS  83 

Review  of  Decimal  Fractions 

Written  Work 

1.  In  a  recent  year  1,591,311,371  dozen  eggs  were  produced 
in  the  United  States.  The  following  decimals  show  the  fractional 
part   of    this   number   produced    in   the    different    geographical 

sections. 

New  England 035 

Middle  Atlantic 102 

East  North  Central 247 

West  North  Central 28 

South  Atlantic 086 

East  South  Central 081 

West  South  Central        .     • 104 

Mountain 022 

Pacific 043 

Find  the  number  of  dozen  eggs  produced  in  each  section,  and 
tabulate  this  on  a  ruled  form.  How  can  you  check  the  accuracy 
of  your  work  ? 

2.  The  value  of  the  wool  produced  by  the  mountain  states  in 
1909  was  .608  more  than  the  value  of  the  wool  produced  by  these 
states  in  1899.  The  increase  in  dollars  was  $  11,039,843.  What 
was  the  value  in  1899  ?     In  1909  ?  • 

3.  The  mountain  states  include  a  large  portion  of  the  grazing 
land  of  the  country  and  for  this  reason  produce  a  large  part  of  the 
wool  of  the  countr3^  In  1909  they  produced  .4332  of  the  total 
value  of  the  wool  grown  in  the  United  States.  By  referring  to 
your  results  in  the  preceding  problem,  find  the  total  value  of  the 
wool  grown  in  the  United  States  in  1909. 

4."  In  1909  Wyoming  produced  the  largest  value  of  wool  grown 
in  any  state  of  the  Union.  The  value  of  its  product  was 
18,912,608.  This  was  what  decimal  part  of  the  value  of  the 
wool  product  of  the  entire  country  for  the  year  ? 

5.  Montana,  the  second  largest  producer  of  wool,  raised  wool 
valued  at  18,223,754.     Ohio,  the  third  largest  producer,  raised 


84  DECIMAL  FRACTIONS 

wool  valued  at  $6,749,005.     Fill  in  the  blanks  in  the  following 
sentences  with  the  proper  decimal  fractions: 

Wyoming  produced times  as  much  wool  as  Montana. 

Ohio  produced as  much  wool  as  Wyoming. 

6.  If  a  boy's  average  gain  in  weight  is  8.25  lb.  per  year,  how 
much  will  he  gain  in  weight  in  2^  yr.  ? 

7.  If  one  turn  of  a  screw  advances  the  point  .14  in.,  how  far 
will  7  turns  advance  it  ? 

8.  A  gallon  of  milk  weighs  8.622  lb.  and  a  gallon  of  water 
weighs  8.355  lb.  How  much  more  does  J  gal.  of  milk  weigh 
than  }  gal.  of  water  ? 

9.  A  boy  can  run  100  yd.  in  11.2  sec.  At  this  rate,  how  long 
would  it  take  him  to  run  80  yd.  ? 

10.  In  a  certain  city  the  rainfall  during  March  was  2.46  in., 
during  April  3.15  in.,  and  during  May  1.09  in.  Find  the  average 
for  these  months. 

11.  A  man  sold  24  dozen  eggs,  which  was  .4  of  all  that  he  had. 
How  many  did  he  have  ? 

12.  If  .375  of  an  acre  of  land  sells  for  |48,  what  should  2| 
acres  sell  for,  at  the  same  rate  ? 

13.  An  English  pound  contains  113.00001  grains  of  pure  gold, 
and  an  American  gold  dollar  contains  23.22  grains  of  pure  gold. 
Find  the  value  of  an  English  pound  in  American  money. 


CHAPTER   IX 
SHORT  METHODS  INVOLVING  ALIQUOT  PARTS 
69.    Equivalent  Common  and  Decimal  Fractions  in  Frequent  Use. 


.50  =  f 

•12|  =  i. 

•06i  =  ,V 

•62i  =  |. 

.331  =  J. 

•iH  =  i 

.05=,V 

.75  =  1. 

.25  =  i. 

•10  =  tV 

.40  =  |. 

.80  =|. 

.20  =  1 

•09i\=xV 

.37J  =  |. 

.83J  =  f. 

.16-1  =  1 

■m=iV 

.60  =  f. 

•87HI- 

.14f  =  f 

•06|  =  iV 

Commit  these  common  fractions  and  their  equivalent  decimals 
to  memory,  as  they  can  be  used  to  shorten  many  computations.^ 

70.   A  Short  Method  of  Multiplying  by  These  Fractions. 

Which  is  easier,  1218  x  .16|  =  208  ;  or  i  of  1248  =  208  ? 

State  a  short  method  of  multiplying  by  each  of  the   decimal 
fractions  in  the  table  above. 

Oral  Work 
Multiply: 

1.    642  X  .50.  2.  936  x  .33J. 

3.    488  X  .25.  4.  650  x  .20. 

5.    366  X  .16f.  6.  840  x  .14f . 

7.    720  X  .121.  8.  456  x  .08f 

9.    930  X  .06|.  10.  320  x  .06^ 

The  results  in  the  preceding  exercise  are  integers.     The  same 
method  may  be  used  when  the  division  results  in  a  fraction. 

Example.     Multiply  4634  by  .25. 

Solution.  .25  =  I. 

4634  -4-  4  =  1158.5. 
85 


86  ALIQUOT  PARTS 

Oral  Work 
Without  copying,  find  the  results  of  the  following: 

1.    8735  X  .50.  2.  3940  x  .33j. 

3.    267  X  .25.  4.  379.3  x  .16f. 

5.    842  X. 20.  6.  3824  x.Hf 

7.    5316  X  .121-.  8.  4026  x  .08J. 

9.    1848  X  .06f.  10.  1940  x  .06|. 

11.    35.69  X.33J.  12.  649.3  X. 25, 

13.    .8347  X  .50.  14.  723.68  x  .20. 

15.    36.92  x.l4f  16.  56.82  X. 121 

17..  7836  X  Ml.  18.  1223  x  .16f. 

19.  3380  X. 062. 

20.  Find  the  value  of  each  of  the  following: 

48  lb.  at  371^  per  pound.  30  yd.  at  62^^  per  yard. 

32  lb.  at  12 J  ^  per  pound.  21  lb.  at  14|^  per  pound. 

21  lb.  at  871^  per  pound.  48  yd.  at  6f  ^  per  yard. 

24  yd.  at  12|  ^  per  yard.  96  lb.  at  83^^  per  pound. 

71.    A  Short  Method  of  Dividing  by  These  Fractions. 

Which  is  easier,  6  ^  .25  =  24  ;  or  6  x  4  =  24  ? 

State  a  short  method  of  dividing  by  each  of  the  decimal  frac 
tions  in  the  table  on  page  85. 

Oral  Work 
Without  copying,  state  the  results  of  the  following : 

2.    49^.50. 
4.    63-^.14f. 
6.    10^.' 


1. 

7-5-.12|. 

3. 

126  -f-  .33J. 

5. 

8-4-.06|. 

7. 

15-^.25. 

9. 

13.63  ^.1( 

11. 

3.249  -^  .50, 

13. 

63.98-*-. 2. 

8. 

1627^.20. 

10. 

1.43^.25. 

12. 

.023-5-.08J 

14. 

.043h-.16|, 

SHORT  METHODS  87 

72.    Aliquot  Parts  which  are  not  Unit  Fractions. 

State  a  short  method  of  multiplying  by  .37  J  ;  by  .66| ;  by  .75 ; 
by  .871. 

State  a  short  method  of  dividing  by  .37 J;  by  .66^;  by  .75; 
by  .87^. 

When  dividing  by  one  number  and  multiplying  by  another, 
observe  the  following  directions: 

Divide  first  if  the  division  results  in  an  integer.  If  the  division 
would  result  m  a  mixed  number^  multiply  first. 

Examples.     1.    Multiply  32  by  .37i. 

Solution.    .37^  =  |. 
32  -  8  =  4. 
*     4  X  3  =  12.     Since  8  is  a  factor  of  32,  the  division  is  performed 
first. 

2.    Divide  16  by  .37|. 

Solution.     Substituting  the  equivalent  common  fraction,  we  have 
16-4-1  =  ? 
or  16  X  f  =  ?     Inverting  the  divisor. 

16  X  8  =  128. 
128  -^  3  =  42|.     Since  3  is  not  a  factor  of  16,  the  multiplication  is  per 
formed  first. 

What  advantage  is  there  in  observing  these  directions  ? 

Written  Work 
Without  recopying,  find  the  results  of  the  following  : 


1. 

64  X  .375. 

2. 

96  X  .66f. 

3. 

480  X  .75. 

4. 

168  X  .875. 

5. 

248  X  .87|-. 

6. 

3260  X  .75. 

7. 

4864  X  .37J. 

8. 

639x.66f. 

9. 

42-^.37^. 

10. 

56 -.871 

11. 

40^.66|. 

12. 

36  ^  .75. 

13. 

1462 -.662. 

14. 

465 -.375. 

15. 

11322 -.75. 

16. 

994 -.875. 

17. 

426  X  .875. 

18. 

143  X  .371. 

19. 

1347  X  .75. 

20. 

539  X  .66f. 

21. 

3.29  X  .75. 

22. 

1.267  X  .875. 

23. 

139 -^.87J. 

24. 

1426-^.37^. 

25. 

139  ^.66|. 

26. 

46-f-.75. 

27. 

46.9 -^.37^. 

28. 

.429 -f-.66t. 

88 


ALIQUOT  PARTS 


73.  General  Table  of  Aliquot  Parts.     The  following  table  shows 
the  most  frequently  used  decimal  parts  of  1,  10,  100,  and  1000. 


Fractions 

i 

§ 

§ 

i 

i 

i 

i 

of  1 

.50 

.331 

.66f 

.25 

.75 

.125 

.375 

of  10 

5. 

3.33^ 

6.66 1 

2.5 

7.5 

1.25 

3.75 

of  100 

50. 

33.33i 

66.66f 

25. 

75. 

12.5 

37.5 

of  1000 

500. 

333^ 

666| 

250. 

750. 

125. 

375. 

Fractions 

i 

1 

1 

A 

A 

iV 

h 

f 

of  1 

.625 

m 

.875 

.081- 

.061 

.06i 

.161 

.141 

of  10 

6.25 

8.33i 

8.75 

■m 

.625 

IM 

1.42 

of  100 

62.5 

83.3i 

87.5 

8.3i 

6.25 

16f 

•14.28 

of  1000 

625. 

833.3^ 

875. 

83i 

62.5 

166| 

142.8 

Study  this  table  until  you  can  recognize  quickly  these  fractional 
parts  of  1,  10,  100,  and  1000. 


74.    Rules  for  Multiplication  by  Aliquot  Parts  of  1,  10,  100,  and 
1000. 

a.  To  multiply  by  fractional  parts  of  10. 

Multiply  by  the  equivalent  fraction ;  multiply  this  product  by  10,  by  moi>- 
ing  the  decimal  point  one  place  to  the  rights  annexing  a  zero,  if  necessary. 

Examples.     1.    Multiply  16  by  2^. 

Solution.     2|  is  I  of  10.     ^  of  16  =  4.     Multiply  by  10,  by  annexing  a 
zero ;  the  result  is  40. 

2.    Multiply  26  by  1.25. 

Solution.    1.25  is  ^  of  10.     \  of  26  =  3.25.     Move  the  decimal  point  one 
place  to  the  right;  the  result  is  32.5. 

b.  To  multiply  by  fractional  parts  of  100. 

Multiply  by  the  equivaleyit  common  fraction;  multiply  this  product  by 
100. 


I 


SHORT  METHODS  89 

Examples.     1.     Multiply  24  by  871. 

Solution.  87^  is  |  of  100. 

I  of  24  =  21. 
21  X  100  =  2100. 

2.    Multiply  4252  by  12.5. 

Solution.  12.5  is  |  of  100. 

I  of  4252  =  531.5. 
531.5  X  100  =  53,150. 

Oral  Work 
State  a  short  method  of  multiplying  by  each  of  the  following : 


.06i; 

2.50; 

6|; 

m-' 

250; 

87J; 

6.25; 

37  J; 

7.60; 

5; 

3831; 

75; 

125; 

8^; 

^■' 

12.50; 

H' 

62|; 

H' 

8|; 

25; 

66*; 

375; 

750; 

875; 

37.50; 

7500; 

12,500. 

Find  the  products  of  the  following.  Do  the  work  orally  when 
possible.  Be  prepared  to  explain  how  the  short"  method  was  ap- 
plied in  each  example. 


1. 

32  X  25. 

2. 

Ill  X  3f 

3. 

390  X  66|. 

4. 

648  X  250. 

5. 

724  X  75. 

6. 

832  X  1^. 

7. 

96  X  871. 

8. 

108  X  83f 

9. 

3264  X  .625. 

10. 

144  X  8J. 

11. 

80  X  875. 

12. 

48  X  375. 

13. 

464  X  12.50. 

14. 

24  X  71 

15. 

3.20x25. 

16. 

.27  X  6f . 

17. 

8.4  X  3.75. 

18. 

640  X  6.25. 

19. 

3.612  x.83f 

20. 

208  X  3f . 

21. 

143  X  250. 

22. 

1936  X  62.50. 

23. 

1721  X  7.50. 

24. 

1239  X  125. 

26. 

426  X  750. 

75.  Interchanging  Multiplicand  and  Multiplier.  When  the  mul- 
tiplicand and  multiplier  are  abstract  numbers,  they  may  be  inter- 
changed. 

Example.     Multiply  25  by  428. 

Solution.     Interchanging,  428  x  25 

i  of  428  =  107. 
107  X  100  =  10,700. 


90  ALIQUOT  PARTS 

Written  Work 

Perform  the  following  multiplications  as  indicated.      Explain 
how  the  short  method  was  applied  in  each  example. 

1.  924x12.50.    2.  864x750.      3.  125x488. 

4.  264  X  .12|.     5.  45  X  .06|.      6.  250  x  3288. 

7.    62.50x648.  8.  8J  x  3.60.  9.  342x87.50. 

10.    375  X  112.  11.  6|  X  456.  12.  1468  x  250. 

13.    875  X  88.  14.  1250  x  96.  15.  1776  x  .625. 

16.    7.2  X  8f.  17.  li  X  104.  18.  125  x  1.248. 

19.    66  X  875.  20.  83^  x  9.6.  21.  62^  x  20. 

Find  the  cost  of  the  following: 

22.  12  articles  at  $.50  each 
16  articles  at  .25  each 
18  articles  at  .33 J  each 
30  articles  at     .40    each 

16  articles  at     .75    each   

Total 

23.  64  doz.  articles  at  $  .62^  per  dozen 
76  doz.  articles  at  8.75  per  dozen 
58    doz.  articles  at      .75    per  dozen 

125    doz.  articles  at       .16    per  dozen 

6^  doz.  articles  at      .32    per  dozen      ____^ 
Total 

24.  72  lb.  at  I  .83^  per  pound 
52  lb.  at  1.25  per  pound 
44  lb.  at  .37 J  per  pound 
90  lb.  at       .12J  per  pound 

112  lb.  at       .06 J  per  pound     

Total 

25.  80  yd.  at  I  .621- per  yard 
66|  yd.  at  1.20  per  yard 
86  yd.  at  1.25  per  yard 
25    yd.  at       .78    per  yard 

75    yd.  at       ,66^  per  yard     ^^^ 
Total 


SHORT  METHODS  91 

26.  83^  yd.    at  11.80  per  yard 
12^  doz.  at    1.60  per  dozen 

8|  lb.     at     1.60  per  pound 
6|  yd.    at     2.10  per  yard 

3 J  yd.    at     1.80  per  yard     

Total 

27.  135  yd.  at  1. 06 J  per  yard 

56  yd.  at  .08|  per  yard 

96  yd.  at  .16|  per  yard 

152  yd.  at  .12|-  per  yard 

24  yd.  at  .07 J  per  yard 

Total 

76.    Rules  for  Division  by  Aliquot  Parts  of  1,  10,  100,  1000. 

a.  To  divide  by  fractional  parts  of  1. 
Divide  by  the  equivalent  common  fraction. 

Example.     Divide  13  by  .121  Solution.     .12\  =  I 

13  -^  i  =  13  X  f  =  104. 

b.  To  divide  by  fractional  parts  of  10. 

Divide  by  10  ;  divide  this  quotient  by  the  equivalent  common  fraction. 

Example.     Divide  80  by  2.50.  Solution.    2.50  is  \  of  10. 

80  -  10  =  8. 

8  -  J  =  8  X  f  =  32. 

c.  To  divide  by  fractional  parts  of  100. 

Divide  by  100 ;  divide  this  quotient  by  the  equivalent  common  fraction. 

Oral  Work    . 

1.  State  a  rule  for  dividing  by  fractional  parts  of  1000. 

2.  1 100  will  pay  for  how  many  articles  at  i  .33^  each  ? 

3.  112  will  pay  for  how  many  yards  of  cloth  at  $.25  per 
yard? 

4.  Which  is  easier  — 

14-^.75=?  or  14--|=? 

5.  State  how  to  find  the  total  cost  of  some  articles,  when  the 
number  of  articles  bought  is  given  and  the  cost  of  each  is  S^^  ; 

uy-,  siy;  wy-,  uy-,  62y;  siy. 


92 


ALIQUOT   PARTS 


Without   copying,  state   results  for   the   following   examples. 
State  the  method  of  operation  in  each. 

6.    15-^.121.  7.    14-f-.061. 

8.    9^.25.  9.    $6-^1.75. 

10.    114 ^1.87 J.  11.    $8^$1.33J. 

State  the  quotients  of  each  of  the  following  : 


] 

Dividend         Divisor 

Quotient                            Dividend 

Divisor         Qxtotibnt 

12. 

42            .331 

13.     13 

.25 

14. 

22             .66f 

15.    36 

.75 

16. 

5        *     .061 

17.    45 

.371 

18. 

17             .125 

19.    28 

87.5 

20. 

15          1.25 

21.    900 

6.25 

22. 

400         8. 33  J 

23.     150 
Written  Work 

.06| 

Complete  the  following : 

Total  Cost                                        Pkicb  Each 

1.    $     5.25                         $  .371         -^ 

NUMBKB  PtTKCUASED 

2. 

20.25 

.75 

3. 

56.00 

.66f 

4. 

40.00 

1.25 

5. 

77.00 

.871 

6. 

212.50 

2.50 

7. 

97.50 

3.75 

8. 

Divide  each  of  the  following  by  .12| : 
.37^;    .33J;    .625;    .871;    .25: 

;  1.14f 

9.    Find  the  sum 
decimally. 

of  J,  |,  |,  |,  |,  and  J  and  express  the  sum 

10. 

Divide  36  by  each  of  the  following : 
.37J;     .12^;     .14?;     .50; 

.06f 

SHORT  METHODS  93 

11.    How  many  yards  can  be  bought  in  each  case  : 

Total  Cost  Cost  per  Yard  Numbbe  of  Yards 


116 

$  .25 

24 

.33i 

36 

.371        • 

20 

.621 

32 

.50 

26 

.66| 

56 

1.25 

44 

1.33-1 

24 

2.66f 

Review  of  Short  Methods 

Perform  the  following  operations,  telling 

what 

;  short  method 

was  used  in  each  case : 

1. 

360-^.37  J. 

2. 

f  +  |. 

3. 

436  X  11. 

4. 

65  X  25. 

5. 

463  X  287. 

6. 

1016  X  1005. 

7. 

3654  X  2700. 

8. 

105  X  126. 

9. 

95  X  87. 

10. 

i-i- 

11. 

48{  X  63 1. 

12. 

611  X  121. 

13. 

109  X  113. 

14. 

A  +  tV 

15. 

463  X  416. 

16. 

96  X  94. 

17. 

1015  X  1014. 

18. 

13  X  18. 

19. 

61  X  4J. 

20. 

825  X  927. 

21. 

.000825x100. 

22. 

17x12. 

23. 

724  X  999. 

24. 

116  X  104. 

25. 

i^h 

26. 

113  X  102. 

27. 

1026  X  1003. 

28 

i  +  h 

29. 

5362  X  111. 

30. 

433  X  99. 

31. 

109  X  112. 

32. 

976  X  990. 

33. 

331  X  121 

34. 

17  X  19. 

35. 

131  X  14f . 

36. 

f  +  f 

37. 

f-l- 

38. 

151x181 

39. 

96  X  88. 

40. 

905.387  X  3000. 

41. 

986  X  993. 

42. 

16  X  18. 

43. 

874  X  1236. 

UNITS   OF  MEASURE   AND   THEIR  APPLICATIONS 

CHAPTER  X 

DENOMINATE  NUMBERS 
Tables  of  Weights  and  Measures 

77.  Long  Measure. 

12  inches  (in.)  =  1  foot  (ft.) 

3  feet  =  1  yard  (yd.) 

5|^  yards,  or  16J  feet  =  1  rod  (rd.) 
320  rods,  or  5280  feet  =  1  mile  (mi.) 
1760  yards  =  1  mile 

Architects,  carpenters,  and  mechanics  frequently  write  '  for  foot,  and  "  for 
inch.     Thus  8'  7"  means  8  ft.  7  in. 

In  engineering  it  is  customary  to  divide  the  foot  and  the  inch  into  tenths 
and  hundredths,  instead  of  into  halves  and  fourths.  There  is  a  growing  tend- 
ency to  use  the  decimal  division  of  the  units. 

Other  measures  of  length  are  : 

1  hand      =  4  in.     Used  in  measuring  the  height  of  horses. 

1  fathom  =  6  ft.     Used  in  measuring  depths  at  sea. 

1  knot,  nautical  or  geographical  mile  =  1.1526f  mi.  or  6086  ft. 

The  knot  is  used  in  measuring  distances  at  sea.  It  is  equivalent  to  1  min.  of 
longitude  at  the  equator. 

78.  Square  Measure. 

144  square  inches  (sq.  in.)=  1  square  foot  (sq.  ft.) 

9  square  feet  =  1  square  yard  (sq.  yd.) 

30 J  square  yards  =  1  square  rod  (sq.  rd.) 

160  square  rods  =  1  acre  (A.) 

640  acres  =  1  square  mile  (sq.  mi.) 

Sq.  '  and  sq.  "  are  frequently  used  for  square  foot  and  square  inch.  Thus, 
15  sq.  '  6  sq.  "  means  15  sq.  ft.  6  sq.  in. 

A  square  is  100  sq.  ft.     It  is  used  in  measuring  roofing. 

94 


TABLES  OF  WEIGHTS  AND   MEASURES  95 

79.  Cubic  Measure. 

1728  cubic  inches  (cu.  in.)=s  1  cubic  foot  (cu.  ft.) 
27  cubic  feet  =  1  cubic  yard  (cu.  yd.) 

128  cubic  feet  =  1  cord 

A  cubic  yard  (of  earth)  is  considered  a  load. 
24|  cubic  feet  =  1  perch  (P.) 

A  perch  of  stone  or  masonry  is  16J  ft.  (1  rd.)  long,  IJ  ft.  wide, 
and  1  ft.  high. 

80.  Avoirdupois  Weight. 

16  ounces  (oz.)=  1  pound  (lb.) 
100  pounds  =  1  hundredweight  (cwt.) 

2000  pounds  =  1  short  ton  (T.) 

2240  pounds  =  1  long  ton  (T.) 

Avoirdupois  weight  is  used  in  weighing  all  ordinary  substances 
except  precious  metals,  jewels,  and  drugs  at  retail. 

The  long  ton  is  used  in  mining  and  in  the  United  States  custom- 
house. 

81.  Liquid  Measure. 

4  gills  (gi.)  =  lpint  (pt.) 
2  pints  =  1  quart  (qt.) 

4  quarts        =  1  gallon  (gal.) 

A  gallon  contains  231  cu.  in. 

31.5  gal.  are  considered  1  barrel  (bbl.). 

63  gal.  =  1  hogshead  (hhd.). 

82.  Dry  Measure. 

2  pints  (pt.)  =  1  quart  (qt.) 
8  quarts  =  1  peck  (pk.) 
4  pecks  =  1  bushel  (bu.) 

A  bushel  contains  2150.42  cu.  in. 
A  dry  quart  contains  67.2  cu.  in. 
A  liquid  quart  contains  57.75  cu.  in. 


96  DENOMINATE  NUMBERS 

83.    Measures  of  Time. 

60  seconds  (sec.)=  1  minute  (min.) 


60  minutes 

=  1  hour  (hr.) 

24  hours 

=  1  day  (da.) 

7  days 

=  1  week  (wk.) 

30  days 

=  1  commercial  month  (mo.) 

52  weeks 

=  1  year  (yr.) 

12  months 

=  1  year 

360  days 

=  1  commercial  year 

365  days 

=  1  common  year 

366  days 

=  1  leap  year 

100  years 

=  1  century 

84.  Counting. 

12  units  =  1  dozen  (doz.) 

12  dozen  =1  gross  (gro.) 

12  gross  =  1  great  gross  (gr.  gro.) 

20  units  =  1  score 

85.  Wood  Measure. 

A  straight  pile  of  wood,  4  ft.  x  4  ft.  x  1  ft.,  contains  1  cord  foot. 
8  cord  feet,  or  128  cubic  feet  =  1  cord. 

86.  United  States  Money. 

10  mills     =  1  cent 
10  cents    =  1  dime 
10  dimes  =  1  dollar 
10  dollars  =  1  eagle 

The  mill  is  not  a  coin,  but  the  term  is  frequently  used  in  com- 
putations.    The  term  "  eagle  "  is  not  common  in  business. 

87.  English  Money. 

4  farthings  (far.)  =  l  penny  ((?.),  (plural,  "pence") 
12  pence  =  1  shilling  (s. )  =  $ .  243+ 

20  shillings  =  1  pound  sterling  (£),  $4.8665 


DENOMINATE  NUMBERS  97 

88.  French  Money. 

100  centimes  (c.)=  1  franc  (fr.) 
A  franc  is  worth  about  1 .193. 

89.  German  Money. 

100  pfennigs  (pf.)=  1  mark  (M.) 
A  mark  is  worth  about  f  0.238. 

Written  Work 

1.  Draw  a  line  1  foot  long  at  the  blackboard.  Try  to  form  a. 
very  definite  mental  picture  of  this  length  so  that  you  may  be  able 
to  estimate  lengths  with  a  fair  degree  of  accuracy. 

2.  Draw  lines  of  the  following  lengths  without  any  aid,  then 
check  each  estimate. 

^ft,  2  ft.,  3  ft.,  I  ft.,  1|  ft.,  7  ft.,  3  in.,  9  in.,  15  in. 

3.  Estimate  the  length  and  width  of  your  desk  ;  the  length  and 
width  and  height  of  the  classroom  ;  the  dimensions  of  the  school 
building  and  grounds.     Check  your  estimates. 

4.  Practice  estimating  and  stepping  off  various  distances  until 
you  can  do  so  with  a  fair  degree  of  accuracy. 

5.  Lay  off  on  the  school  grounds  a  square  rod  and,  if  possible, 
an  acre.  Estimate  the  areas  of  various  lots,  parks,  or  fields,  and 
check  your  results,  when  possible. 

6.  By  lifting  various  units  of  weights  and  then  checking  your 
own  estimates  of  the  weights  of  numerous  objects,  you  can 
acquire  the  ability  to  estimate  certain  weights  with  but  a  small 
error. 

90.  Changing  to  Lower  Denominations. 
Example.      How  many  quarts  in  3  bu.  3  pk.  5  qt.  ? 

•  Solution.  3  bu.  =  12  pk. 

12  pk.  +  8  pk.  =  1.5  pk. 

1.5  pk.  =120qt. 

120  qt.  +  5  qt.  =  125  qt. 

Therefore,  3  bu.  3  pk.  5  qt.  =  125  qt. 

After  studying  this  solution,  state  a  method  for  reducing 
measured  quantities  to  lower  denominations. 


98  DENOMINATE  NUMBERS 

Oral  Work 
Reduce  as  indicated  ;  do  as  much  of  the  work  orally  as  possible. 

1.  15^  yd.  to  feet. 

2.  4|  ft.  to  inches. 

3.  5  gal.  3  qt.  1  pt.  to  pints. 

4.  4  bu.  3  pk.  5  qt.  to  quarts. 

5.  5  lb.  9  oz.  to  ounces  (avoir.). 

Example.     Reduce  .345  mi.  to  lower  denominations. 

Solution.  1  mi.  =  320  rd. 

.345  mi.  =  110.4  rd. 
1  rd.  =■  5.5  yd. 
.4  rd.  =:  2.2  yd. 
1  yd.  =  3  ft. 
.2  yd.  =  .6  ft. 
1  ft.  =  12  Id. 
.6  ft.  =  7.2  in. 
Therefore,  .345  mi.  =  110  rd.  2  yd.  0  ft.  7.2  in. 

After  studying  this  solution,  state  a  method  for  reducing  frac- 
tions of  a  large  denomination  to  units  of  lower  denominations. 

Written  Work 
Reduce  : 

1.    I  mi.  to  rods.  2.    .236  mi.  to  feet. 

3.    .89  bu.  to  quarts.  4.    ^  sq.  mi.  to  square  rods. 

5.    62  rd.  to  feet.  6.    .85  gal.  to  pints. 

7.  4.3  mi.  to  feet. 

8.  A  man  bought  an  acre  of  land  and  sold  it  in  building  lots  of 
10  sq.  rd.  each.     How  many  lots  did  he  sell  ? 

91.  Changing  to  Higher  Denominations.  When  a  quantity  is 
expressed  in  a  low  denomination,  it  may  be  desired  to  express  it 
in  higher  denominations. 


DENOMINATE  NUMBERS  99 

Examples.     1.    Express  1316  pints  in  higher  denominations. 

Solution.     Since  2  pints  =  1  quart, 

1316  pints  =  658  quarts. 
Since  4  quarts  =  1  gallon, 

658  quarts  =  164  gals.,  and  2  qt.  remaining. 
Therefore,    1316  pints  =  164  gal.,  2  qt. 

After  studying  this  solution,  state  a  method  for  reducing  quan- 
tities to  units  of  higher  denominations. 

2.    Reduce  3  qt.  1  pt.  to  a  decimal  part  of  a  peck. 

Solution.  3  qt.  1  pt.  =  7  pt. 

1  pk.  =  16  pt. 
Therefore,  3  qt.  1  pt.  =  j\  pk. 

f  J  pk.  =  .4375  pk. 

Written  Work 
Reduce  to  units  of  higher  denominations : 
1.    367  pints  (dry  measure).  2.    133  in.  3.    47  ft. 

4.    12  yd.  5.    216  oz.  (avoir.). 

6.    31  pt.  (liquid  measure).  7.    2369  sq.  in. 

8.  Reduce  4  sq.  ft.  68  sq.  in.  to  a  decimal  part  of  a  square  rod. 

9.  Reduce  1  qt.  2  pt.  to  a  decimal  part  of  a  gallon. 

10.  Reduce  7  oz.  to  a  decimal  part  of  a  pound  (avoir.). 

11.  Reduce  |  yd.  to  a  decimal  part  of  a  rod. 

12.  Reduce  2^  ft.  to  a  decimal  part  of  a  yard. 

13.  Reduce  47  sq.  rd.  to  a  decimal  part  of  an  acre. 

14.  Reduce  8 J  in.  to  a  decimal  part  of  a  foot. 

15.  Reduce  2 J  qt.  to  a  decimal  part  of  a  gallon. 

16.  Reduce  4  ft.  7  in.  to  a  decimal  part  of  a  rod. 

92.    Addition  of  Denominate  Numbers. 

Example.     Find  the  sum  of  2  yd.  2  ft.  9  in.  and  4  yd.  1  ft.  7  in, 

Solution.  2  yd.    2  ft.      9  in. 


6  yd.     3  ft.     16  in. 

•7    «         \    (i  4    " 


State  a  method  for  adding  denominate  numbers. 


100  DENOMINATE  NUMBERS 


Written  Work 

Add: 

1.    2yr. 

5  mo.     18  da. 

2.    5  gal. 

3  qt.     1  pt. 

5  " 

8    "       19  " 

4    " 

2   "      1  ^' 

6  " 

11    "        13   " 

5    " 

1     u         1    u 

3.    2  1b. 

5  oz.     17  pwt. 

4.     5  A. 

126  sq.  rd. 

3  " 

8  "      19    " 

16  " 

249  "     " 

4  " 

9  "       12    " 

13  » 

168  "     " 

3.    7  mo. 

12  da. 

6.    12  mi. 

4rd. 

5    " 

5  " 

8   " 

9  " 

7.  A  rectangular  field  is  18  rd.  2  yd.  2  ft.  long,  and  13  rd.  1  yd. 
2|-  ft.  wide.  What  length  of  wire  will  be  required  for  a  fence 
6  wires  high  ? 

8.  A  dealer  bought  17  gal.  3  qt.  of  milk  from  each  of  two  men, 
and  29  gal.  3  qt.  1  pt.  from  a  third  man.  What  was  the  entire 
cost  at  19  cents  a  gallon  ? 

93.    Subtraction  of  Denominate  Numbers. 

If  it  is  required  to  subtract  1  mi.  42  rd.  13  ft.  from  3  mi.  25  rd. 
14  ft.,  we  write  the  numbers  as  follows  ; 

3  mi.     25  rd.     14  ft. 
1    "       42  "       13  " 


When,  as  in  this  problem,  the  number  of  units  of  some  denom- 
ination of  the  minuend  is  smaller  than  the  number  of  correspond- 
ing units  of  the  subtrahend,  combine  one  unit  of  the  next  larger 
denomination  with  the  number  of  units  of  the  minuend.  The 
problem  thus  becomes : 

2  mi.     345  rd.     14  ft. 
1    "         42  "       13  " 
1   "       303  "         1  " 


DENOMINATE  NUMBEI^  ,>,   i     -  .,,,,,^.101 

'  >         5     1  )      ^    - 

Written  Work 
Subtract  as  indicated  : 

1.    13  bu.     3pk.     2qt.  2.    7  A.     5  sq.  rd.     6  sq.  ft. 

g      44  Y      44  44  2      ''  '' 


6   " 

2    " 

7   " 

27  rd. 
13  " 

4  yd. 

5  " 

1ft. 

19  1b. 

7  " 

12  oz. 
14  " 

4.    14  gal.     2  qt.     1  pt. 
5    "        3   " 


6.  A  man  owned  a  field  containing  1|  A.  From  it  he  sold 
two  lots  each  having  an  area  of  11|  sq.  rd.  What  was  the  area  of 
the  part  remaining  ? 

7.  From  a  cask  which  contained  31  gal.  3  qt.  1  pt.  of  vinegar, 
19  gal.  3  pt.  were  drawn  out.     How  much  remained  ? 

94.   Multiplication  Involving  Denominate  Numbers. 
Example.     Multiply  3  yd.  2  ft.  7  in.  by  4. 
Solution.  3  yd.    2  ft.      7  in. 


12  yd.     8  ft.     28  in. 
or     15  yd.     1  ft.      4  in. 


Written  Work 
Multiply  as  indicated : 

1.  5  gal.  3  qt.  1  pt.  by  7.  2.   7  lb.  5  oz.  by  12. 

3.  5  cu.  yd.  19  cu.  ft.  364  cu.  in.  by  13. 

4.  4  mi.  19  rd.  3  yd.  by  18. 

95.   Division  Involving  Denominate  Numbers. 
Examples.     1.    Divide  4568  inches  by  8. 

Solution.  4568  in.  -^  8  =  571  in. 

571  in.  =  2  rd.  8  yd.  2  ft.  7  in. 

2.  Divide  17  gal.  2  qt.  1  pt.  by  3. 

Solution.  17  gal.  2  qt.  1  pt.  =  141  pt. 

141  pt.  -r-  3  =  47  pt. 
47  pt.  =  5  gal.  3  qt.  1  pt. 


102  DENOMINATE   NUMBERS 

3.    How  many  times  is  4  gal.  2  qt.  contained  in  1  barrel  ? 

Solution.  4  gal.  2  qt.  =  18  qt. 

1  bbl.  =  126  qt. 
126  qt.  contains  18  qt.  7  times. 

Explain  the  method  used  in  this  illustration. 

Written  Work 
Divide  as  indicated: 

1.  27  cu.  yd.  15  cu.  ft.  -^6. 

2.  584  A.  8  sq.  rd.  -^  8. 

3.  1  sq.  ft.  48  sq.  in  ^  16. 

4.  How  many  times  are  4  yd.  2  ft.  7  in.  contained  in  29  yd. 
6  in.  ? 

5.  Reduce  to  the  decimal  part  of  a  mile:  5  rd.;  7 J  rd.;  5  ft.; 
13  yd.;  5  ft.  9  in. 

6.  An  automobile  traveled  1  mi.  in  3|^  min.     What  was  the 
rate  per  hour  ? 

7.  If  a  man  sells  17  loads  of  wheat,  each  containing  53  bu. 
8  pk.,  at  97^  cents  a  bushel,  how  much  should  he  receive  ? 

8.  Fifteen  cans  hold  an  average  of  10  gal.  2  qt.  1  pt.     How 
much  do  they  all  hold  ? 

9.  Change  .427  sq.  mi.  to  units  of  lower  denominations. 

10.  A  cubic  foot  of  water  weighs  62.5  lb.,  cast  iron  weighs 
about  7.2  as  much  as  water;  what  is  the  weight  of  2|  cu.  ft.  of 
cast  iron  ? 

11.  Determine  whether  the  window  space  in  your  school  room 
is  as  much  as  J  of  the  floor  space.  It  should  be  at  least  ^  in  a 
well-lighted  room. 

12.  A  train  leaves  a  city  at  4  :  30  p.m.,  and  reaches  a  certain 
station  87  J  mi.  distant  at  6  :  20  p.m.  Allowing  12  min.  for  station 
stops,  what  is  the  rate  of  travel  per  hour  ? 

13.  There  are  twenty-four  students  in  a  class  and  each  needs  2J 
cups  of  hot  water  for  a  cooking  lesson.  How  much  water  must 
there  be  in  a  kettle  to  supply  all  the  class  at  one  time,  allowing 
4  cups  to  a  quart  ? 


CHAPTER   XI 
THE   METRIC  SYSTEM 

The  metric  system  of  weights  and  measures  originated  in  France 
about  1800.  An  international  convention  met  at  Paris  in  1799 
and  adopted  the  system,  but  it  was  not  until  forty  years  later 
that  it  came  into  general  use  in  France.  Since  that  time  its  use 
has  become  universal  in  scientific  measurements,  and  it  is  estab- 
lished as  the  commercial  system  in  a  large  part  of  the  civilized 
world.  The  United  States  made  the  metric  system  "lawful"  in 
1866,  and  obligatory  in  Porto  Rico  and  the  Philippine  Islands 
about  1900.  The  advantage  of  the  metric  system  lies  in  the  fact 
that  it  is  based  on  a  decimal  scale.  The  only  multiplier  or  divisor 
used  is  10  or  a  power  of  10.  All  reductions  are  made  by  merely 
changing  the  position  of  the  decimal  point. 

96.  Definitions  of  Terms.  The  unit  of  length  is  the  meter.  It 
is  approximately  39.37  inches. 

The  unit  of  capacity  is  the  liter  (leter),  which  is  equivalent  to  a 
cube  having  an  edge  one-tenth  of  a  meter  long. 

The  unit  of  weight  is  the  gram,  which  is  the  weight  of  a  cube  of 
distilled  water  having  an  edge  of  ^o  o  ^^  ^  meter. 

97.  Fractions  and  Multiples  of  Units. 

Fractional  parts  of  these  units  are  expressed  by  Latin  prefixes, 
as  follows:  ,^illi.  _  ^^^  thousandth 

centi-  =  one  hundredth, 
deci-    =  one  tenth. 

Multiples  of  the  units  are  expressed  by  Greek  prefixes,  as 
follows:  ^^k^.   ^^^^^ 

hekto-  =  one  hundred, 
kilo-     =  one  thousand, 
myria-  =  ten  thousand. 
103 


104 


THE  METRIC  SYSTEM 


Thus, 


a  millimeter  is  .001  of  a  meter, 
a  milligram  is  .001  of  a  gram, 
a  centigram  is  .01  of  a  gram, 
a  dekaliter  is  10  liters. 


The  prefixes  and  their  meanings  should  be  learned. 


98.    Measures  of  Length. 

1  millimeter  (mm.) 
1  centimeter  (cm.) 
1  decimeter  (dm.) 
1  METER  (m.) 
1  dekameter  (Dm.) 
1  hektometer  (Hra.) 
1  kilometer  (Km.) 
1  myriameter 

The  table  may  be  expressed  as 
10  millimeters 
10  centimeters 
10  decimeters 
10  meters 
10  dekameters 
10  hektometers 


=  .001  of  a  meter. 
=  .01  of  a  meter. 
=  .1  of  a  meter. 
=  1  meter. 
=  10  meters. 
=  100  meters.  • 
=  1000  meters. 
=  10,000  meters. 

follows: 

=  1  centimeter. 

=  1  decimeter. 

=  1  meter. 

=  1  dekameter. 

=  1  hektometer. 

=  1  kilometer. 


The  following  rule  is  10  centimeters,  or  1  decimeter,  long.     The 
smallest  subdivisions  are  millimeters. 


Illllllllilllllllllllllll 


llllllllllllllllllllllllllll  lllllllll 


mMH 


MI 


CENTIMETERS 
INCHES 


ilililiMlilililililililililililililililililili'ililiiililihli 


The  meter  is  used  for  measuring  certain  merchandise  and  for 
otner  purposes  where  the  foot  and  yard  would  be  used  in  the 
English  system.  It  is  also  used  in  engineering  and  constructions. 
The  kilometer  is  used  for  measuring  distances  which  would  be 
expressed  in  the  English  system  in  miles. 


THE  METRIC  SYSTEM  105 

The  centimeter  is  used  instead  of  the  inch  in  certain  measure- 
ments such  as  in  expressing  the  size  of  paper  and  books.  The 
millimeter  is  used  for  very  fine  measurements  in  machine  con^ 
struction  and  similar  work. 

Examples.     1.     Reduce  473  m.  to  Km. 
Solution.  473  m.  =  ,473  Km. 

2.  Reduce  .54  Km.  to  m. 

Solution.  .54  Km.  =  540  m. 

Oral  Work 

1.  Reduce  734  m.  to  Hm.;   Km.;  dm. 

2.  Reduce  .042  Km.  to  cm.;   Hm.;  mm. 

3.  Reduce  5427  cm.  to  m.;  Km. 

4.  Reduce  .0037  Km.  to  cm. 

5.  Reduce  4.72  Km.  to  dm. 

6.  Reduce  .034  m.  to  Km. 

7.  Reduce  1^  cm.  to  mm. 

8.  Reduce  .0842  Km.  to  m. 

The  advantage  of  the  metric  system  is  well  illustrated  in  the 
measurements  of  distances.  A  distance  of  1  kilometer,  6  deka- 
meters,  4  decimeters,  8  centimeters,  is  expressed  as  1060.48  meters, 
and  is  read  "ten  hundred  sixty  meters  and  forty-eight  centi- 
meters, just  as  we  would  say  "ten  hundred  sixty  dollars  and 
forty-eight  cents." 

99.    Measures  of  Area. 

The  table  of  area  is  formed  by  squaring  the  units  of  length,  as 
in  the  English  system. 

100  sq.  millimeters  (sq.  mm.)  =  1  sq.  centimeter  (sq.  cm.). 
100  sq.  centimeters  =  1  sq.  decimeter  (sq.  dm.). 

100  sq.  decimeters  =1  sq.  meter  (sq.  m.). 

100  sq.  meters  =  1  sq.  dekameter  (sq.  Dm.). 

100  sq.  dekameters  =  1  sq.  hektometer  (sq.   Hm.). 

100  sq.  hektometers  =  1  sq.  kilometer  (sq.  Km.) 


106  THE  METRIC  SYSTEM 

The  abbreviations  of  the  system  are  not  uniform,  mm. 2  is  fre- 
quently used  instead  of  sq.  mm.;  etc. 

The  more  commonly  used  denominations  of  square  measure  are 
square  kilometer  (sq.  Km.),  square  meter  (sq.  m.),  square  centi- 
meter (sq.  cm.),  and  square  millimeter  (sq.  mm.) 

The  square  meter  is  used  to  measure  such  surfaces  as  those  to 
which  the  square  yard  would  apply;  the  square  centimeter  is 
used  to  measure  smaller  surfaces. 

100.  Land  Measure. 

The  are  is  ten  meters  square.     It  has  a  side  about  33  feet  long. 

The  hektare,  containing  100  ares,  is  about  2|  acres.  The 
hektare  is  the  unit  of  land  measure.  A  quarter  section  (160  acres) 
is  almost  exactly  64  hektares. 

Examples.     1.    Reduce  .4867  sq.  m.  to  sq.  Hm. 
Solution.  4367  sq.  m.  =  .4367  sq.  Hm. 

2.    Reduce  .0547  sq.  Dm.  to  sq.  dm. 
Solution.  .0547  sq.  Dm.  =  547  sq.  dm. 

Oral  Work 

1.  Reduce  427  sq.  m.  to  sq.  Dm;  sq.  Hm. 

2.  Reduce  87  sq.  cm.  to  sq.  m. ;   sq.  mm. 

3.  Reduce  .0854  sq.  Hm.  to  sq.  m.;  sq.  Dm. 

4.  Reduce  .1  sq.  m.  to  sq.  cm.;  sq.  mm. 

Written  Work 
Complete    the   following,    carrying    results    to    three   decimal 
p  aces  ;  -j^  square  meter  =  ?  square  inches. 

1  square  meter  =  ?  square  yards. 

1  square  meter  =  ?  square  feet. 

1  square  centimeter  =  ?  square  feet. 
1  square  foot  =  ?  square  meters. 

1  square  yard  =  ?  square  meters. 

101.  Measures  of  Volume. 

The  cubic  meter  is  the  unit  of  volume.  It  is  sometimes  called 
the  stare. 


THE  METRIC  SYSTEM  107 

1000  cu.  millimeters  (cu.  mm.)  =  1  cu.  centimeter  (cu.  cm.) 
1000  cu.  centimeters  =  1  cu.  decimeter  (cu.  dm.) 

1000  cu.  decimeters  =  1  cu.  meter  (cu.  m.) 

1000  cu.  meters  =  1  cu.  dekameter  (cu.  Dm.) 

1000  cu.  dekameters  =  1  cu.  hektometer  (cu.  Hm.) 

1000  cu.  hektometers  =  1  cu.  kilometer  (cu.  Km.) 

The  abbreviations  mm. 3,  cm. 3,  etc.  are  sometimes  used. 

Examples.     1.    Reduce  4386  cu.  m.  to  cu.  Dm. 
Solution.    4386  cu.  m.  =  4.386  cu.  Dm. 
2.    Reduce  .0427  cu.  cm.  to  cu.  mm. 
Solution.     .0427  cu.  cm.  =  42.7  cu.  ram. 

Oral  Work 

1.  Reduce  37864  cu.  m.  to  cu.  Dm. 

2.  Reduce  .04276  cu.  cm.  to  cu.  mm. 

3.  Reduce  742863  cu.  dm.  to  cu.  Dm. 

4.  Reduce  .0476  cu.  m.  to  cu.  cm. 

Written  Work 

A  meter  is  approximately  39.37  inches.     Complete  the  following 
table    of  comparisons  : 

1  cubic  meter  =  ?  cubic  inches. 
1  cubic  meter  =  ?  cubic  feet. 
1  cubic  meter  =  ?  cubic  yards. 
1  cubic  foot     =  ?  cubic  meters. 
1  cubic  yard    =  ?  cubic  meters. 

102.    Measures  of  Capacity. 

The  unit  of  capacity  is  the  liter,  which  is  a  cubic  decimeter. 
It  equals  1.05668  liquid  quarts  or  0.9081  dry  quart. 

10  milliliters  (ml.)      =  1  centiliter  (cl.) 
10  centiliters  =  1  deciliter  (dl.) 

10  deciliters  =1  liter  (1.) 

10  LITERS  =  1  dekaliter  (Dl.) 

10  dekaliters  =  1  hektoliter  (HI.) 

10  hektoliters  =  1  kiloliter  (Kl.) 


108  THE  METRIC  SYSTEM 

The  liter  serves  the  same  purpose  in  measuring  capacities  as 
the  quart  and  gallon.  The  hektoliter  is  used  for  measuring 
quantities  commonly  measured  by  the  bushel  in  countries  where 
the  English  system  is  used. 

Oral  Work 

1.  Reduce  427  1.  to  DL;  HI.;  cl. 

2.  Reduce  .043  Dl.  to  dl.;  cl. 

3.  Reduce  .04278  Kl.  to.  1. ;  dl. ;  HI. 

Written  Work 
Complete  the  following  table  of  comparisons  : 
1  peck  =  ?  liters. 

,  1  bushel        =  ?  liters. 
1  bushel        =  ?  hektoliters. 
1  hektoliter  =  ?  bushels  ? 

103.    Measures  of  Weight. 

The  gram  is  the  unit  of  weight.  A  liter  of  water  weighs  a 
kilogram,  or  1000  grams. 

10  milligrams  C^g-)  =  1  centigram  (eg). 

10  centigrams  =  1  decigram  (dg.) 

10  decigrams  =  1  gram  (g.) 

10  grams  =  1  dekagram  (Dg.) 

10  dekagrams  =  1  hektogram  (Hg.) 

10  hektograms  =  1  kilogram  (Kg.) 

Oral  Work 

1.  Reduce  4736  g.  to  Kg.;  eg.;   mg. 

2.  Reduce  .03  eg.  to  mg.;  g.;  Dg. 

3.  Reduce  .07428  Kg.  to  g.;  dg.;  eg. 

Written  Work 
A  kilogram  =  2.204622  pounds  avoirdupois. 
Complete  the  following  table  of  comparisons : 

1  gram         =  ?  pound  avoirdupois. 

1  gram         =  ?  ounce  avoirdupois. 

1  kilogram  =  ?  ounces  avoirdupois. 

1  pound       =  ?  kilograms. 


THE    METRIC  SYSTEM 


109 


The  kilogram  and  the  "  half  kilo "  are  the  common  measures 
used  in  trade.     A  half  kilo  =  ?  pounds. 

The  metric  ton  or  tonneau  (1000  kilograms)  is  used  for  larger  weights. 

1  metric  ton  =  ?  pounds 
1  metric  ton  =  ?  short  tons. 
1  metric  ton  =  ?  long  tons. 

104.    Comparative  Table  of  Weights  and  Measures. 

The  following  table  of  comparisons  will  be  useful  in  reducing 
measurements  stated  in  the  English  system  to  equivalent  metric 
measures,  and  vice  versa.     It  is  not  to  be  memorized. 


1  inch 

=  25.4001    millimeters,    or    2.54001   centi- 

meters. 

1  foot 

=  .304801  meter. 

1  yard 

=  .914402  meter. 

1  mile 

=  1.60935  kilometers. 

1  square  inch 

=  945.16  square  millimeters,  or  6.452  square 

centimeters. 

1  square  foot 

=  .09290  square  meter. 

1  square  yard 

=  .8361  square  meter. 

1  square  mile 

=  2.59  square  kilometers. 

1  cubic  inch 

=  16,387.2    cubic    millimeters    or    16.3872 

cubic  centimeters. 

1  cubic  foot 

=  .02832  cubic  meter. 

1  cubic  yard 

=  .7646  cubic  meter. 

1  acre 

=  .4047  hectare. 

1  liquid  quart 

=  .94636  liter. 

1  liquid  gallon 

=  3.78543  liters. 

1  dry  quart 

=  1.1012  liters. 

1  peck 

=  8.80982  liters. 

1  bushel 

=  .35239  hectoliter. 

1  grain 

=  .06480  gram. 

1  ounce  (avoir.) 

=  28.3495  grams. 

1  ounce  (Troy) 

=  31.10348  grains. 

1  pound  (avoir.) 

=  .45359  kilogram. 

1  pound  (Troy) 

=  .37324  kilogram. 

1  millimeter 

=  .03937  inch. 

no 


THE  METRIC  SYSTEM 


1  centimeter 

1  meter 

1  meter 

1  meter 

1  kilometer 

1  square  millimeter 

1  square  centimeter 

1  square  meter 

1  square  kilometer 

1  cubic  centimeter 

1  cubic  meter 

1  hectare 

1  milliliter 

1  liter 

1  liter 

1  hectoliter 

1  gram 

1  kilogram 


=  .3937  inch. 

=  39.37  inches. 

=  3.28083  feet. 

=  1.093611  yards. 

=  .62137  mile. 

=  .00155  square  inch. 

=  .155  square  inch. 

=  10.764  square  feet  or  1.196  square  yards, 

=  .3861  square  mile. 

=  .061  cubic  inch. 

=  35.314  cubic  feet,  or  1.3079  cubic  yards. 

=  2.471  acres. 

=  .03381  liquid  ounce  or  .2705  apothecaries' 

dram. 
=  1.05668  liquid  quarts,  or  .26417  liquid 

gallon. 
=  .9081  dry  quart. 
=  2.83774  bushels. 
=  15.4324  grains,  or  .03527  ounce  (avoir.), 

or  .03215  ounce  (Troy). 
=  2.20462    pounds    (avoir.),    or    2.67923 

pounds  (Troy). 


Exercise 

State  the  result  in  each  of  the  following  in  metric  units.     (Use 
a  meter  stick  in  making  the  measurements.) 

1.  Measure  the  edges  of  the  cover  of  this  book. 

2.  How  many  square  centimeters  in  the  surface  of  the  cover? 

3.  How  tall  are  you  ? 

4.  Find  the  dimensions  of  the  top  of  your  desk. 

5.  What  is  the  length  of  your  classroom  ?    What  is  its  width? 
Estimate  its  height. 

6.  What  is  the  area  of  the  floor  ? 

(Other  measurements  may  be  suggested  by  the  teacher). 

7.  Make  a  cube  from  cardboard  which  will  contain  1  liter. 


THE  METRIC  SYSTEM  111 

Using  the  table  of  comparative  weights  and  measures,  make 
the  following  reductions : 

8.  1  ft.  8  in.,  to  meters. 

9.  3|  meters  to  feet  and  inches. 

10.  6  sq.  ft.  to  square  meters. 

11.  14  square  meters  to  square  yards. 

12.  36  cubic  inches  to  cubic  centimeters. 

13.  130  cubic  centimeters  to  cubic  inches. 

14.  A  bin  is  8  ft.  x  16  ft.  x  7  ft.  How  many  cubic  meters  will 
it  contain  ? 

15.  A  horse  weighs  715  kilograms.  How  many  pounds  does  he 
weigh  ? 

16.  The  distance  from  Boston  to  Chicago  by  rail  is  999  miles. 
How  many  kilometers  ? 

17.  What  is  the  cost  of  16  yards  of  cloth  at  il.35  per  meter? 

18.  A  barrel  (31.5  gal.)  will  contain  how  many  liters? 

19.  If  a  stere  is  -^j  of  a  cord,  how  many  steres  are  there  in  a 
wood  pile  4  ft.  X  4  ft.  x  17  ft.  ? 

20.  How  long  would  a  tank  4  feet  wide  and  3  feet  high  have 
to  be  to  contain  6  cubic  meters  ?  (State  your  result  to  the  near- 
est foot). 

21.  The  Eiffel  tower  in  Paris  is  about  300  m.  high.  State  this 
height  in  feet  ? 

22.  Olive  oil  weighs  .92  as  much  as  an  equal  volume  of  water. 
What  is  the  weight  of  1  liter  of  olive  oil  ? 

23.  If  a  stream  flows  at  the  rate  of  1|^  Km.  per  hour,  what  is 
its  rate  of  flow  per  second  ?     Express  the  result  in  centimeters. 

24.  A  liter  of  mercury  weighs  13.596  Kg.  How  many  mm^. 
of  mercury  weigh  3  g.  ? 

25.  Fifty-four  miles  are  how  many  kilometers,  to  the  nearest 
unit? 

26.  428  ft.  are  how  many  meters,  to  the  nearest  unit  ? 

27.  Sound  travels  332  m.  per  second,  how  long  will  it  take  it 
to  travel  4.5  Km.  ? 


CHAPTER  XII 


PRACTICAL   BUSINESS   MEASUREMENTS 


Plane  Figures 


105.    Rectilinear  Figures.     An  angle  is  the  opening  between  two 

lines  which  meet. 

Thus  the  angle  AOB  is  formed  by 
the  lines  AG  and    OB^   which  meet 
(intersect)  at  0. 
The  lines  which  intersect  are  called  the  arms  of  the  angle  and 
their  point  of  intersection  is  called  the  vertex  of  the  angle. 

Thus  AG  and  GB  are  the  arms  of  the  angle  and  G  is  the  vertex. 

Two  angles  which  have    the  same  vertex  and  a  common  arm 

between  them  are  called  adjacent  angles. 

Thus  the  angles  ^  OX  and  XOFare 

adjacent  angles.  i 

A  right  angle  is  an  angle  formed  when 
one  straight  line  meets  another  straight  line  so  as  to  make  the  ad- 
jacent angles  equal.  The  lines  forming  the  angles  are  said  to  be 
^  perpendicular  to  each  other. 

Thus  the  angles  MGX  and  XGA 
are  right  angles  and  the  lines  AM 
_j^    and  GX  are  perpendicular  to  each 
^  other. 

An  acute  angle  is  an  angle  less  than  a  right  angle. 
An  obtuse  angle  is  an  angle  greater  than  a  right  angle. 
Thus  the  angle  ADB  is  acute  and 
the  angle  BDO'i'^  obtuse. 

A  surface  has  length  and  breadth 
but  no  thickness. 

A  plane,  or  plane  surface,  is  a  level  surface  such  as  that  of  still 
water. 

112 


PRACTICAL  BUSINESS  MEASUREMENTS 


113 


A  plane  figure  is  a  figure  all  of  whose  points  lie  in  the  same  plane. 
A  quadrilateral  is  a  plane  figure  bounded  by  four  straight  lines. 
A   parallelogram  is   a   quadrilateral  whose  opposite  sides   are 
parallel. 

A  rectangle  is  a  parallelogram  whose  angles  are  right  angles. 
A  square  is  a  rectangle  whose  sides  are  all  equal. 


Parallelogram 


Rectangle 


A  diagonal  of  a  quadrilateral  is  the  straight  line  connecting  two 
of  its  opposite  vertices. 

A  triangle  is  a  plane  figure  bounded  by 
three  straight  lines. 

A  right  triangle  is  one  that  has  a  right 
angle. 

The  hypotenuse  of  a  right  triangle  is  the 
side  opposite  the  right  angle. 

A  triangle  which  has  three  sides  equal  is  called  equilateral.  If 
two  sides  are  equal  it  is  called  isosceles.  If  it  has  no  equal  sides 
it  is  called  scalene. 


The  perimeter  of  a  plane  figure  is  the  sum  of  its  sides. 

A  circle  is  a  plane  figure  bounded  by  a  curved  line  called  the 
circumference,  every  point  of  which  is  equally  distant  from  a 
point  within  called  the  center. 


114  PRACTICAL  BUSINESS  MEASUREMENTS 

The  diameter  of  a  circle  is  a  straight  line  passing  through  the 
center  and  terminated  by  the  circumference. 

^,*cxxnifere^„  The  ladlus  of  a  circle  is  the  straight  line 

©from  the  center  of  the  circle  to  the  circumfer- 
ence.   It  is  equal  to  one  half  of  the  diameter. 
An  arc  of  a  circle  is  any  part  of  the  circum- 
ference. 
The  base  of  a  plane  figure  is  the  side  on 
which  it  is  supposed  to  stand. 
The  altitude  of  a  plane  figure  is  the  perpendicular  distance  from 
the  highest  point  above  the  base  to  the  base  or  to  the  base  pro- 
duced. 

An  area  is  always  expressed  in  terms  of  some  square  unit,  such 
as  square  inch,  square  foot,  or  square  yard. 

To  find  the  area  of  any  figure  is  to  find  the  number  of  square 
units  it  contains. 

A  square  whose  side  is  one  unit  is  said  to  have  an  area  of  one 
square  unit.  Thus,  a  square  whose  side  is  one  inch  has  an  area 
of  one  square  inch. 

Oral  Work 

1.  Into  how  many  squares  1  in.  on  a  side  can  you  divide  a 
rectangle  5  in.  long  and  1  in.  wide  ? 

2.  Into  how  many  squares  1  in.  on  a  side  can  you  divide  a 
rectangle  5  in.  long  and  3  in.  wide  ? 

3.  How  many  square  feet  in  the  area  of  a  rectangle  7  ft.  long 
and  3  ft.  wide  ? 

Areas  of  Plane  Figures 

Tlie  number  of  square  units  in  the  area  of  a  rectangle  is  equal  to  the 
number  of  units  in  the  length  times  the  number  of  units  in  the  width. 

Find  the  areas  of  the  rectangles  having  the  following  di- 
mensions : 

4.  12  ft.  by  8  ft.  5.    3|  rd.  by  6  rd. 
6.    25  rd.  by  25  rd.  7.    11  in.  by  15  in. 
8.    15  in.  by  15  in.                             9.    35  rd.  by  35  rd. 

10.    16  ft.  by  12  ft.  11.    3.5  ft.  by  3.5  ft. 


PRACTICAL   BUSINESS   MEASUREMENTS 


115 


Written  Work 

1.  How  many  acres  are  there  in  a  rectangular  field  130  rd. 
long  and  80  rd.  wide  ? 

2.  Find  the  cost  of  painting  a  rectangular  floor  30  ft.  long 
and  18  ft.  wide  at  80  cents  a  square  yard. 

3.  A  rectangular  floor  24  ft.  long  and  22  ft.  wide  is  to  be 
covered  with  tiles  8  in.  square.     How  many  tiles  will  be  required? 

4.  A  football  field  is  120  yards  long  and  53^  yards  wide. 
How  many  acres  does  it  contain  ? 

5.  A  tennis  court  is  78  ft.  long  and  36  ft.  wide.  What  part 
of  an  acre  does  it  contain  ? 

6.  A  field  96  rd.'by  130  rd.  produces  2340  bu.  of  wheat. 
What  is  the  average  yield  per  acre  ? 

7.  Find  the  area  of  a  square  field  whose  perimeter  is  128  rd. 

8.  A  rectangular  field  is  42  rd.  long  and  26  rd.  wide.  Find 
the  cost  of  fencing  it  at  $1.20  a  rod. 

9.  Find  the  cost  of  painting  the  four  walls  of  a  room  14  ft. 
long,  10  ft.  6  in.  wide,  and  9  ft.  high  at  8  cents  per  square  yard,  no 
allowance  being  made  for  openings. 

The  parallelogram  ABCB  may 
be  shown  to  be  equivalent  to  the 
rectangle  AMRD  by  cutting  off 
the  area  H  and  placing  it  in  the 
position  H' 

It  is  evident  that  the  rule  for 
finding  the  area  of  a  parallelogram  is  the  same  as  for  finding  the 

area  of  a  rectangle.     State 
the  rule. 

A  triangle  may  be  shown 
to  be  equivalent  to  one 
half  the  area  of  a  rec- 
tangle with  the  same  base 
and  altitude. 

The  number  of  square  units  in  the  area  of  a  triangle  is  equal  to  one  half 
the  number  of  units  in  the  base  times  the  number  of  U7iits  in  the  altitude. 


116  PRACTICAL  BUSINESS   MEASUREMENTS 

Oral  Work 

State  the  area  of  the  triangles  whose  bases  and  the  altitudes  are 
as  follows  : 

Bask  Altitude  Bask  Altitude 

2.  12  rd.  7  rd. 

4.  101ft.  12  ft. 

6.  1  ft.  4  in.  9  in. 

8.  4  ft.  6  in.  20  in. 

106.  Circumference  and  Area  of  a  Circle.  Find  the  length  of  the 
circumferences  of  several  circles  of  different  sizes.  This  may  be 
done  as  follows: 

Mark  a  point  on  the  circumference  and  roll  the  circle  along  a 
level  surface.  Determine  the  distance  between  the  places  where 
the  point  comes  in  contact  with  the  level  surface. 


1. 

10  ft. 

6  ft. 

3. 

4.2  rd. 

20  rd. 

5. 

18  yd. 

11  yd. 

7. 

3  yd.  1  ft. 

2^  ft. 

In  the  figure  above,  the  length  of  the  line  PB  is  equal  to  the 
length  of  the  circumference  of  the  circle. 

After  the  circumferences  of  several  circles  of  different  sizes  have 
been  measured,  find  the  ratio  of  the  length  of  the  circumference  of 
each  circle  to  the  length  of  its  diameter.  Find  the  average  of 
these  ratios.  If  the  measurements  were  made  with  care  you  will 
find  that,  whatever  the  radius  of  the  circle,  the  length  of  the  circum- 
ference divided  by  the  length  of  the  diameter  gives  a  quotient 
slightly  larger  than  three.  It  is  shown  in  geometry  that  the 
ratio  is  always  the  same  and  that  it  is  approximately  3.1416  or 
^^.  This  constant  ratio  is  called  tt  (pronounced  pi).  Length  of 
circumference  -^  length  of  diameter  =  tt. 

C 
This  is  usually  expressed  as  follows:   —  =  tt,  or  C=  ttD, 


PRACTICAL  BUSINESS  MEASUREMENTS  117 

If  the  diameter  of  a  circle  is  known,  the  circumferences  may  be 
found  by  multiplying  the  diameter  by  the  value  of  tt. 

If  the  circumference  is  known,  the  diameter  may  be  found  by 
dividing  the  circumference  by  the  value  of  tt. 

Note.    For  most  practical  purposes  ^-^  may  be  used  as  the  value  of  tt. 

Written  Work 

Find  the  circumferences  of  the  circles  with  the  following 
diameters : 

1.    16  ft.  2.    32  in.  3.    18  yd.  4.    3  ft.  4  in. 

5.    9  ft.  2  in.         6.    110  yd.  7.    2  rd.  8.    6  ft.  8  in. 

9.    2  rd.  1  yd.     10.    7  ft.  2.5  in. 

Find  the  diameters  of  circles  with  the  following  circumferences: 
11.    110  yd.  12.    44  ft.  13.    5000  ft. 

14.    5  ft.  6  in.  15.    1  mi. 

16.  A  bicycle  wheel  has  a  diameter  of  28  in.  How  many  times 
will  the  wheel  turn  in  going  1  mile  ? 

17.  The  inner  circumference  of  a  circular  race  track  is  one 
mile.  The  track  is  90  ft.  wide.  How  long  is  the  outer  circum- 
ference ? 

If  a  circle  be  divided  as  shown  in  the  figure  below,  it  is  evident 
that  the  circle  is  composed  of  figures  which  are  approximately 
triangles.  The  area  of  the  circle  is  equal  to  the  sum  of  the  areas 
of  the  approximate  triangles. 

The  altitude  of  each  of  the  triangles  is  equal  to  the  radius  of  the 
circle,  and  the  sum  of  the  bases  of  the  triangles  is  equal  to  the 
circumference  of  the  circle. 

We  may  conclude,  therefore,  that  the  number  of  units  in  the  area 
of  the  circle  is  equal  to  one  half  the  number  of  units  in  the  drcum- 
ference^  times  the  number  of  units  in  the  radius. 


118  PRACTICAL  BUSINESS  MEASUREMENTS 

Tins   may   be   expressed   as   follows :    area   of   circle  =  — , 

where  Q  represents  the  number  of  units  in  the  circumference  and 
It  the  number  of  units  in  the  radius. 

Since  (7=  ttD,  or  2  ttB,  the  area  is  equal  to  ^"^^  ^  ^^  or  ttW. 

Hence,  to  find  the  area  of  a  circle^  square  the  radius  and  multiply 
the  result  hy  tt. 

Note.  The  parts  into  which  the  circle  is  divided  are  not  exact  triangles  but  it 
is  proved  in  geometry  that  the  area  of  the  circle  is  the  same  as  that  of  a  triangle 
having  a  base  equal  to  the  circumference  and  an  altitude  equal  to  the  radius. 

Written  Work 

1.  Find  the  area  of  a  circle  the  radius  of  which  is  6  ft. 

2.  Find  the  area  of  a  circle  the  radius  of  which  is  12  ft.     Com- 
pare with  the  preceding  area. 

3.  Find  the  cost  of  painting  a  circular  area  fiaving  a  diameter 
of  1\  ft.  at  75  cents  per  square  yard. 

4.  Find  the  area  inclosed  by  a  circular  running  track  with  an 
inner  circumference  of  |  mi. 

5.  Find  the  area  of  a  circular  window  6  ft.  in  diameter. 

6.  Find  the  cost  of  refinishing  the  top  of  a  circular  table  which 
has  a  diameter  of  4  ft.  4  in.,  at  25  cents  per  square  foot. 

Compute  the  areas  of  the  following: 

7.  A  triangle  having  a  base  of  11    in.    and   an   altitude    of 
9  in. 

8.  A  parallelogram  having  a  base  of  12  in.  and  an  altitude  of 
3.5  in. 

9.  A  circle  having  a  radius  of  3  ft.  7  in. 

10.  A  circle  having  a  circumference  of  14  ft.  3  in. 

11.  A  rectangle  having  an  altitude  of  7.5  ft.,  and  a  base  of 
3.45  ft. 

12.  A  triangle  having  an  altitude  of  4  rd.  3  yd.,  and  a  base  of 
12.3  rd. 


PRACTICAL  BUSINESS  MEASUREMENTS 


119 


13.  A  square  which  has  a  perimeter  of  14.72  in. 

14.  What  must  you  know  and  what  must  you  do  to  find  the 


area  of  each  of  the  following:  circle;  square; 
gram;  rectangle  ? 


triangle;  parallelo- 


Land  Measure 
107.    Description  of  Farm  Lands. 

When  the  land  of  the  Central  and  Western  states  was  surveyed 
the  following  methods  were  employed  : 

a.  Imaginary  lines  running  north  and  south  were  established 
and  called  principal  meridians.  These  principal  meridians  were 
numbered  from  1  to  24.  The  first  runs  through  Ohio  and  the  last 
through  Oregon. 

h.  Imaginar}^  lines  running  east  and  west  were  also  established, 
and  called  base  lines. 

N 


Base 


Line 


6  mi." 


c.  Lines  were  then  run  at  intervals  of  six  miles  parallel  to  the 
principal  meridians,  and  others  at  intervals  of  six  miles  parallel  to 
the  base  lines. 


120 


PRACTICAL  BUSINESS  MEASUREMENTS 


d.  The  land  was  thus  divided  into  tracts  6  miles  square. 
Each  such  area  is  called  a  township.  The  townships  are  de- 
scribed by  their  relation  to  the  principal  meridians  and  to  the 
base  line. 

The  township  marked  A  is  described  in  real  estate  records 
thus  : 

Twp.  2  N,  R  3  E  of  the *  principal  meridian. 

Twp.  2  N  means  that  it  is  in  the  second  row  of  townships  north 
of  the  base  line  ;  while  R  3  E  means  that  it  is  in  the  third  row 
east  of  the  specified  principal  meridian. 

Description  of  Qi  Twp.  2  S,  R  2  W. 

Describe  townships  marked  D  and  B. 

What  is  meant  by  Twp.  3  N,  R  1  W  ?     Twp.  3  S,  R  2  E  ? 

e.  Each  township  is  divided  into  sections,  one  mile  square. 
Each  section,  therefore,  contains  640  acres.  The  sections  are 
numbered  as  shown  in  the  following  plot. 


6 

5 

4 

3 

2 

1 

7 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

19 

20 

21 

22 

23 

24 

30 

29 

28 

27 

26 

25 

31 

32 

33 

34 

35 

36 

Assuming  that  this  is  a  plot  of  township  A  in  the  figure 
on  page  119,  the  25th  section  would  be  described  as  follows  : 

Section  25,  Twp.  2  N,  R  3  E  of  the principal  meridian. 

Fractions  of  a  section  are  often  sold,  and  the  following  method 
of  description  is  used. 


*  Here  is  stated  the  number  of  the  meridian. 


PRACTICAL  BUSINESS  MEASUREMENTS 


121 


The  section  is  divided  into  quarters. 

M  is  described  as  the  northwest  \  of  Section  25,  Twp.  2  N, 
R3E. 

H  is  described  as  the  southeast  \  of  Section  25,  Twp.  2  N, 
R3E. 

Section  25 


North 

North 

West 
M 

East 
160  Aares 

Q 

South 

South 

West 

East 

0 

H 

If  iff  and  Q  were  sold  together,  they  would  be  described  as  the 
north  I  of  Section  25,  Twp.  2  N,  R  3  E. 

The  following  diagram  shows  a  section  divided  into  various 
farms,  with  their  descriptions. 


Section  25 

N 


W 


West  V2 
Section 

Westy2 
of  , 

N.E./^ 

N.E.H 

of 
N.  E.h 

S.E.H 
of 

N.E.'4 

Southeast 

122  PRACTICAL  BUSINESS  MEASUREMENTS 

Written  Work 

Since  a  section  is  a  mile  square,  each  side  of  the  section  is  320 
rd.  in  length.  S.tate  the  dimensions  of  each  of  the  farms  shown 
in  the  diagram  on  page  121 ;  thus, 

The  west  ^  of  Section  25  is  160  rods  east  and  west  by  320  rods 
north  and  south  and  contains  320  acres. 

108.  Measurements  of  Farm  Lands.  The  unit  of  farm  land 
measure  is  the  acre,  which  contain  160  square  rods. 

Thus,  a  piece  of  land  10  rods  wide  and  16  rods  long  contains  an 
acre,  or  a  strip  of  land  1  rod  wide  and  160  rods  long  contains  an 
acre. 

Oral  Work 

1.  Locate  farms  on  plot  of  Section  25  having  the  following 
dimensions.     How  many  acres  in  each  ? 

a.    160  rods  x  80  rods.  h.    160  rods  x  160  rods. 

c.    320  rods  x  160  rods.  d.    80  rods  x  80  rods. 

2.  The  owner  of  the  southwest  |  sells  a  strip  20  rods  wide 
along  the  south  side  of  his  farm.  How  much  does  he  receive  at 
il50  per  acre?     Describe  the  property  sold. 

3.  The  owner  of  the  S.  E.  {  of  the  N.  E.  ^  sells  the  north  half 
of  his  farm  for  f  125  per  acre. 

How  much  land  did  he  sell  ?  Describe  it.  What  was  the  total 
selling  price  ? 

Square  Root  and  its  Applications 

109.  Extracting  the  Square  Root.  The  square  of  a  number  is  the 
product  obtained  by  using  the  number  twice  as  a  factor.  Thus, 
since  3x3  =  9;  9  is  the  square  of  3. 

The  square  root  of  a  number  is  qne  of  the  two  equal  factors  of 
the  number.  Thus,  the  square  of  4  is  16.  The  square  root  of  16 
is  4. 

The  square  root  of  a  number  may  be  indicated  by  writing  the 
number  under  the  radical  sign  or  by  placing  *'  |  "  above  and  to  the 
right  of  the  number.  Thus,  both  Vl44  and  144-  indicate  the 
square  root  of  144. 


PRACTICAL  BUSINESS  MEASUREMENTS  123 

Oral  Work 

What  is  the  square  root  of  each  of  the  following :  36,  64,  81, 
169,  225,  25,  49,  1,  256,  400,  100,  10,000? 

How  many  digits  in  the  square  of  each  of  the  following :  1,  9, 
10,  99,  100,'  999,  1000,  9999? 

How  does  the  number  of  digits  in  the  square  of  a  number  com- 
pare with  the  number  of  digits  in  the  number  ? 

The  square  of  53  may  be  found  as  follows : 

50  +  3 

50  +  3  502       =   2500 

(50x3) +  32  2(50  X  3)   =     300 

502 +(50x3)  32= 9 

502  +  2(50x3) +32  *                2809 

By  squaring  several  numbers,  as  illustrated  above,  you  will  un- 
derstand that  the  square  of  a  number  is  equal  to  the  square  of  the 
tens,  plus  twice  the  product  of  the  tens  by  the  units^  plus  the  square  of 
the  units. 

This  principle  may  be  applied  in  finding  the  square  root  of 
numbers  whose  square  root  cannot  be  found  by  inspection. 

The  square  of  a  number  contains  twice  as  many  digits,  or  one 
less  than  twice  as  many  digits,  as  the  original  number.  Hence,  if 
an  integer  be  separated  into  groups  or  periods  of  two  digits  each, 
from  right  to  left,  there  will  be  as  many  digits  in  the  square  root 
as  there  are  groups  of  digits  in  the  original  number. 

Example.     Find  the  square  root  of  576. 

Solution.  Beginning  at  the  right,  separate  the  digits  into  groups  of  two 
each.  The  greatest  square  in  5  is  4,  and  the  square  root  of  4  is  2.  .Two  is 
therefore  the  tens  digit  of  the  root.  q  a 

Find  the  remainder  and  annex  the  next  group  (76).  — — 

The  result  is  176.     We  have  taken  the  square  of  the  tens  from  the  "^  '^ 

number,  hence  the  remainder  (176)  must  contain  twice  the  product  of  4 

the  tens  by  the  units  plus  the  square  of  the  units.  Twice  two  tens  is  40'  176 
four  tens  or  40.  40  is  contained  4  times  in  176.  Hence,  4  is  the  units'  4  176 
digit  of  the  root.     Twice  the  tens,  times  the  units,  plus  the  square  of  TT 

the  units,  is  the  same  as  the  sum  of  twice  the  tens,  and  the  units,        ' 

times  the  units.     Therefore,  add  4  units  to  the  40  and  multiply  the  result  by 
4.     The  result  is  then  176.     Therefore,  the  square  root  of  576  is  24. 


124 


PRACTICAL  BUSINESS  MEASUREMENTS 


To  find  the  square  root  of  a  number. 

Begin  at  the  units  and  separate  the  number  into  groups  of  two  digits  each. 
Find  the  greatest  sq^iare  in  the  left-hand  group,  and  write  its  square  root 
for  the  first  digit  of  the  required  root.  Subtract  the  square  of  the  root 
digit  from  the  left-hand  group  and  then  annex  the  second  group  for  a 
dividend. 

Annex  a  zero  to  the  part  of  the  root  already  found  and  multiply  the  re- 
sult by  two.  Divide  the  dividend  by  this  product.  Place  the  quotient  as 
the  next  figure  of  the  root.  Add  the  quotieyit  to  the  divisor  and  multiply  the 
result  by  the  digit  of  the  root  just  found. 

Continue  in  like  manner  until  all  of  the  groups  have  been  used.  The 
result  will  be  the  square  root.  (It  may  not  be  the  exact  square  root,  as 
indicated  in  the  note  on  page  125.) 

If  the  number  contains  a  decimal  fraction,  begin  at  the  decimal  point  and 
separate  the  number  into  groups  of  two  digits  each  ivay  from  the  decimal 
point.  If  the  last  group  on  the  right  of  the  decimal  point  has  but  one  fig- 
ure, annex  a  zero.     Each  decimal  group)  must  contain  two  figures. 

To  find,  the  square  root  of  a  commoii  fraction  ivhose  numerator  and  de- 
nominator are  not  perfect  squares,  first  reduce  the  common  fraction  to  a 
decimal,  then  extract  the  root. 

Examples.    1.     Extract  the  square  root  of  16,641. 

Solution.  2  _?.  _E 

1  66  41 
1 


20 

66 

2 

44 

22 

2241 

240 

9 
249 

2241 

2.    Extract  the  square  root  of  18.0625. 
Solution.  4.  2    5 

18.  06  25 

16 


80 

206 

2 

164 

82 

4225 

840 

5 
845 

4225 

PRACTICAL  BUSINESS   MEASUREMENTS 


125 


Written  Work 


Find  the  square  root  of : 
1.  3325.        2.  9025. 


5.  52.9984, 


9.  .0256. 


6.  .005476. 


10.  3. 


3.  89.25. 

4.  .1764 

7.    5. 

-!■ 

"•!■ 

12.    7. 

Note.  If  a  number  is  not  a  perfect  square,  its  approximate  square  root  may  be 
found  by  placing  the  decimal  point  in  its  proper  place  and  annexing  zeros  to  the 
right  of  ohe  last  digit.  It  is  usually  not  necessary  to  find  a  root  to  more  than  two 
or  three  decimal  places. 

110.  The  Square  and  the  Right  Triangle.  Since  the  number  of 
units  in  the  area  of  a  square  is  found  b}^  squaring  the  number  of 
units  in  one  side,  it  follows  that 
the  square  root  of  the  number 
of  units  in  the  area  is  the  number 
of  units  in  one  side. 

It  is  proved  in  geometry  that 
the  square  on  the  hypotenuse  of  a 
right  triangle  is  equal  to  the  sum 
of  the  squares  on  the  other  two 
sides.  This  is  illustrated  in  the 
figure. 

The  length  of  the  hypotenuse 
is  equal  to  the  square  root  of  the 
sum  of  the  squares  on  the  other 
two  sides.  To  find  the  length 
of  either  side,  extract  the  square  root  of  the  difference  between 
the  square  on  the  hypotenuse  and  on  the  other  side. 


'c  o, 

b 


Written  Exercise 
A  square  field  contains  9025  sq.  rd. 


Find  the  length  of  one 


1. 

side. 

2.  The  base  lines  on  a  ball  field  are  each  90  ft.  in  length,  and 
are  at  right  angles  to  each  other.  What  is  the  distance  from 
home  plate  to  second  base  ? 


126  PRACTICAL   BUSINESS  MEASUREMENTS 

3.  A  tennis  court  is  78  ft.  long,  and  36  ft.  wide.  What  is  the 
length  of  the  diagonal  ? 

4.  A  ladder  19  ft.  long  placed  on  level  ground  reaches  13  ft. 
up  a  wall.     How  far  is  the  foot  of  the  ladder  from  the  wall  ? 

5.  The  rafters  of  a  building  are  25  ft.  long.  The  ridge  of  the 
roof  is  18  feet  above  a  line  joining  the  foot  of  the  rafters.  How 
wide  is  the  building  ? 

6.  A  rectangular  corner  lot  is  90  ft.  long  and  60  ft.  wide.  A 
path  runs  diagonally  across  it.  What  distance  is  saved  by  using 
the  path? 

7.  A  guy  rope  80  ft.  long  is  attached  to  a  flagpole  at  a  point 
54  ft.  above  the  ground.  How  far  from  the  foot  of  the  pole  may 
the  rope  be  made  to  touch  the  ground  when  stretched  taut  ? 

111.  To  find  the  area  of  a  triangle  when  the  length  of  each  side  is 
known. 

When  the  altitude  of  a  triangle  is  not  known  but  the  length  of 
the  sides  is  known,  the  area  may  be  found  as  in  the  following : 

Example.  Find  the  area  of  a  triangle  the  sides  of  which  are 
12  ft.,  14  ft.,  and  22  ft. 

Solution.  12  +  14  +  22  =  48. 

^  of  48  =  24. 
24  -  12  =  12. 
24  -  14  =  10. 
24  -  22  =  2. 
24  X  12  X  10  X  2  =  5760. 
V5760  =  75.88,  the  number  of  square  feet  in  the  area. 

Rule. 

From  one  half  the  sum  of  the  three  sides  subtract  each  side  separately. 
Find  the  product  of  the  half  sum  and  of  the  three  remainders.  Extract 
the  square  root  of  this  product.  Tlie  result  is  the  number  of  units  in  the 
area. 

Written  Work 

1.  Find  the  area  of  an  equilateral  triangle  the  sides  of  which 
are  8  inches. 

2.  The  perimeter  of  an  isosceles  triangle  is  28  inches.  One  of 
the  equal  sides  is  9  inches.     Find  the  area. 


PRACTICAL  BUSINESS  MEASUREMENTS  127 

3.  Compare  the  area  of  an  equilateral  triangle  with  a  side  of  4 
inches  with  that  of  one  with  a  side  of  8  inches. 

4.  Find  the  value  at  $160  an  acre  of  a  triangular  field  having 
sides  of  60  rd.,  78  rd.,  and  84  rd.  respectively. 

Roofing 

112.  Roofing  is  generally  measured  by  the  square  of  100  square 
feet. 

Shingles  average  4  in.  in  width,  and  are  usually  laid  4  in.,  4J  in., 
5  in.,  or  5 J  in.  to  the  weather.  A  bunch  of  shingles  contains  250. 
Part  of  a  bunch  is  not  sold. 

The  following  table  shows  the  usual  estimate  per  square. 


>  TO  Weathbb 

NUM] 

BER  PER  Square 

4    in. 

1000 

41  in. 

900 

5    in. 

800 

51  in. 

700 

Slate  varies  in  size.     It  is  usually  16'^  by  24^',  or  Q"  by  12". 

Written  Work 

1.  When  shingles  are  laid  A"  to  the  weather,  how  many  4-in. 
shingles  cover  a  square  foot  ?  How  many  to  the  square  foot  when 
they  are  5^'  to  the  weather  ? 

2.  A  roof  is  42  ft.  long  and  28  ft.  wide  on  each  side.  How 
many  bunches  of  shingles  will  be  required  to  cover  it,  if  the  shingles 
are  laid  5  in.  to  the  weather  ? 

3.  At  ^4.50  a  square  what  will  be  the  cost  of  tinning  a  roof 
22  ft.  by  18  ft.? 

4.  A  roof  is  40  ft.  long  and  30  ft.  wide  on  each  side.  How 
many  shingles,  laid  5  in.  to  the  weather,  will  be  required  to  cover 
it? 

5.  How  many  bundles  of  shingles,  li^id  5  in.  to  the  weather,  will 
be  required  for  a  roof  28  ft.  by  21  ft.  ? 


128 


PRACTICAL  BUSINESS  MEASUREMENTS 


The  pitch  of  a  roof  is  found  by  dividing  the  rise  in  the  rafters 
by  the  width  of  the  base  of  the  gable.     If  the  rafters  rise  10  ft. 


Base  of  Gable 


16  ft. 


and  the  base  of  the  gable  is  40  ft.,  the  pitch  of  the  roof  is  ^. 
pitch  of  I  is  called  the  Gothic  pitch. 

Written  Work 
Find  the  pitch  of  the  roof  in  each  of  the  following  : 


Width  of  Bask 

Height 

45  ft. 

20  ft. 

36  ft. 

18  ft. 

64  ft. 

16  ft. 

20  ft. 

5  ft. 

24  ft. 

15  ft. 

3ight  of  the  gable. 

Width  of  Base 

Pitch  of  Eoof 

50  ft. 

h 

20  ft. 

i 

32  ft. 

Gothic 

Flooring 

113.  Flooring  is  usually  measured  by  the  square  or  by  the 
thousand  square  feet.  There  is  some  waste  when  lumber  is 
"tongued"  and  "grooved."  Dealers  measure  the  width  before 
the  lumber  is  matched.  The  amount  of  waste  depends  upon  the 
width  of  the  lumber.  It  is  customary  to  allow  ^  for  flooring  3  in. 
or  more  in  width  and  J  for  flooring  less,  than  3  in.  in  width. 

Illustration.  How  many  square  feet  of  4-in.  flooring  will  be 
required  for  a  room  28  ft.  by  24  ft.? 

28  X  24  =  672,  the  number  of  square  feet  to  be  covered. 
1^  X  672  sq.  ft.  =  840  sq.  ft.,  the  quantity  required. 


PRACTICAL  BUSINESS   MEASUREMENTS  129 

Written  Work 

1.  A  room  is  24  ft.  by  36  ft.  Find  the  cost  of  the  2|^-in.  floor- 
ing at  $  50  per  thousand  square  feet. 

2.  Compute  the  cost  of  flooring  a  hall  72  ft.  by  50  ft.,  with  4-in. 
lumber  at  $  30  a  thousand,  incidentals  $  28.40  extra. 

3.  How  many  feet  of  4-in.  flooring  will  be  required  for  a  hall 
60  ft.  by  42  ft.? 

4.  What  will  the  4-in.  flooring  for  a  hall  60  ft.  by  42  ft.  cost  at 
$  36  per  thousand  ? 

Plastering,  Papering,  Painting,  Carpeting 

114.  Plastering  is  usually  measured  by  the  square  yard.  There 
is  no  uniform  rule  regarding  allowances  to  be  made  for  openings. 

To  find  the  area  of  the  walls,  multiply  the  perimeter  by  the 
height. 

The  dimensions  of  a  room  are  usually  stated  in  the  following 
order:  length,  breadth,  height. 

Thus  the  dimensions  of  a  room  18  ft.  long,  14  ft.  wide,  and  9  ft. 
6  in.  high  would  be  indicated  as  follows:  18  ft.  x  14  ft.  x  9  ft. 
6  in.  or  18^  x  14^  x  9'  6". 

Wall  paper  is  generally  18  inches  wide.  It  is  sold  by  the  single 
roll  of  8  yards  or  by  the  double  roll  of  16  yards.  Complete  rolls 
must  be  bought.  There  is  no  uniform  procedure  in  making 
allowance  for  openings.  Some  paper  hangers  deduct  the  total 
width  of  all  openings  from  the  perimeter  of  the  room,  and  cover 
the  spaces  about  the  openings  with  the  parts  of  strips  left  from 
the  rolls. 

Painting  is  usually  measured  by  the  square  yard.  It  is  not 
customary  to  make  any  allowance  for  openings. 

Carpet  is  sold  by  the  linear  yard  regardless  of  its  width. 
Ingrain  carpets  are  usually  1  yard  wide,  other  carpets  are  usually 
I  yard  wide. 

Carpets  are  generally  laid  lengthwise  of  the  room.  It  is  some- 
times more  economical  to  lay  a  carpet  crosswise.  Fractional 
lengths,  but  not  fractional  widths,  may  be  bought.  Allowance 
must  sometimes  be  made  for  matching  designs. 


130  PRACTICAL  BUSINESS  MEASUREMENTS 

Written  Work 

The  six  rooms  of  a  house  have  the  following  dimensions  and 
openings:  Living  room,  20'  x  16',  3  windows  3'  x  Q'  6'',  and  two 
doors  3'  6"  x  1'  &'.  Dining  room,  15'  x  13'  6",  2  windows  4'  x  6', 
and  two  doors  3'  6"  x  7'.     Two  bedrooms,  each  14'  6"  x  12'  6", 

2  windows  4'  x  6'  6",  and  2  doors  3'  6"  x  7'.     Kitchen,  15'  x  15'  6", 

3  windows  4'  x  7',  and  2  doors  3'  6"  x  7'.  Bathroom,  10'  6"  x  8'  6", 
1  window  3'  x  5',  1  door  3'  6"  x  7'.  All  rooms  are  9  ft.  high  and 
the  baseboards  are  1  ft.  wide. 

1.  Find  the  cost  of  plastering  the  walls  and  ceiling  of  eacli 
room  at  35  cents  a  square  yard,  allowing  for  one  half  the  openings. 

2.  Find  the  cost  of  papering  the  walls  of  the  living  room  and 
the  dining  room  at  f'l.lO  a  double  roll,  making  one  half  allowance 
for  openings. 

3.  Find  the  cost  of  caicimining  the  ceilings  of  these  two  rooms 
at  60  cents  a  square  yard. 

4.  Find  the  cost  of  papering  the  walls  of  the  two  bedrooms  at 
90  cents  a  double  roll,  making  full  allowance  for  openings. 

5.  How  many  square  yards  of  linoleum  will  be  required  to 
cover  the  floors  of  the  bathroom  and  the  kitchen  ? 

6.  Find  the  cost  of  painting  the  baseboards  in  the  six  rooms, 
at  40  cents  a  square  foot,  allowance  being  made  for  all  openings. 

7.  How  many  gallons  of  paint  will  be  required  for  two  coats  on 
a  building  32  ft.  by  24  ft.  by  18  ft.,  if  the  first  coat  takes  one 
gallon  for  52  sq.  yd.  and  the  second  one  gallon  for  74  sq.  yd.  ? 

Solids 

115.  Rectangular  Solids.  A  solid  has  three  dimensions:  length, 
breadth,  and  thickness. 

A  rectangular  solid  is  bounded  by  six  rectangular  surfaces. 
Such  a  solid  is  called  a  prism. 

The  bases  of  a  prism  are  equal  and  parallel. 

A  cube  is  a  rectangular  solid  having  six  square  faces. 

A   cube    1  unit   long,  1    unit  wide,  and  1  unit  thick  contains 


PRACTICAL    BUSINESS  MEASUREMENTS  131 

1  cubic  unit.  Volumes  are  always  measured  in  terms  of  some 
cubic  unit. 

How  many  cubic  inches  in  a  block  1  in.  long,  1  in.  wide,  and 
1  in.  thick  ?  In  a  prism  5  in.  long,  1  in.  wide,  and  1  in.  thick  ? 
in  a  prism  5  in.  long,  3  in.  wide,  and  1  in.  thick  ?  in  a  prism  5  in. 
long,  3  in.  wide,  and  2  in.  thick  ? 

It  is  evident  that  the  number  of  cubic  units  in  the  volume  of  a  rec- 
tangular solid  is  equal  to  the  product  of  the  number  of  units  in  its 
three  dimensions. 


Written  Work 

Compute  the  volumes  of  the  following; 

1.  A  cube  with  an  edge  of  35  in. 

2.  A  rectangular  solid  7'  x  8'  X  5'  &', 

3.  A  piece  of  ice  2J^  x  1|'  x  9^ 

4.  A  piece  of  timber  22  ft.  long,  1|  ft.  wide,  and  IJ  in.  thick. 

5.  How  many  cubic  feet  of  earth  must  be  removed  in  digging 
a  cellar  20' X  18' x  7'? 

6.  Compute  the  cost  of  a  stone  wall  24  ft.  long,  3.5  ft.  wide, 
and  4  ft.  high  at  $3.65  a  cubic  yard. 

7.  A  swimming  tank  is  44'  by  28'  by  9'.  How  many  cubic 
feet  of  water  does  it  contain  when  filled  to  a  depth  of  4'  ?     8'  ? 

8.  A  ditch  for  some  sewer  pipe  is  to  be  made  1200  yd.  long, 
3  ft.  wide,  and  7  ft.  deep.  Compute  the  cost  of  making  the  exca- 
vation at  28  cents  per  cubic  yard. 

9.  Compute  the  number  of  cubic  feet  of  air  space  allowed 
each  student  in  your  schoolroom. 

10.  Compare  the  volumes  of  two  rectangular  pieces  of  ice 
having  the  same  length  and  breadth,  the  thickness  of  one  being 
twice  that  of  the  other. 

\\,    Compute  the  volume  of  a  rectangular  bin  18'  x  16'  x  7'. 

12.    Find  the  capacity  in  bushels  of  a  grain  elevator  60'  x  42' 
X  24'.     (A  bushel  is  equivalent  to  1\  cu.  ft.) 


132  PRACTICAL  BUSINESS  MEASUREMENTS 

116.  A  cord  of  wood  or  stone  is  a  pile  8  ft.  long,  4  ft.  wide,  and 
4  ft.  high.  It  contains  128  cu.  ft.  In  certain  localities  a  cord  of 
wood  means  a  pile  8  ft.  long,  and  4  ft.  high,  the  price  varying  with 
the  length  of  the  stick. 

Written  Work 

1.  A  pile  of  four-foot  wood  ten  feet  high  and  forty-two  feet 
long  was  cut  from  a  ten-acre  tract.  What  was  the  average  num- 
ber of  cords  per  acre  ? 

2.  How  many  cords  of  wood  in  a  pile  30  ft.  by  4  ft.  by  9  ft.  ? 

3.  How  many  cords  of  4  ft.  wood  in  a  pile  16  ft.  by  8  ft.  by 
12  ft.  ? 

117.  A  cylinder  is  a  solid  bounded  by  two  bases  which  are  equal 
parallel  circles  and  by  a  uniformly  curved  surface. 

The  curved  surface  of  a  cylinder  is  called  its  lateral  surface. 

If  the  lateral  surface  of  a  cylinder  be  exactly  covered  with 
paper  and  the  paper  then  removed,  the  paper  will  be  seen  to  have 
the  form  of  a  rectangle  the  base  of  which  is  the  length  of  the  cir- 
cumference of  the  cylinder  and  the  altitude  is  the  height  of  the 
cylinder. 

Hence,  the  number  of  units  in  the  lateral  area  of  a  cylinder  equals 
the  product  of  the  number  of  units  in  the  circumference  by  the  number 
of  units  in  the  altitude.  To  find  the  entire  surface  of  the  cylinder 
the  areas  of  the  two  circular  bases  must  be  added  to  the  lateral  area. 

It  is  shown  in  geometry  that  the  number  of  units  in  the  volume  of  a 
cylinder  equals  the  product  of  the  number  of  units  in  the  area  of  the 
base  and  the  number  of  units  in  the  altitude. 

Written  Work 

1.  Compute  the  entire  surface  of  a  cylindrical  cup  having  a 
diameter  of  3  in.  and  an  altitude  of  7  in. 

Determine  the  cubic  contents  of  this  cup. 

2.  A  cylindrical  cistern  having  a  radius  of  4|^'  is  filled  with 
water  to  a  depth  of  9'.  How  many  cubic  feet  of  water  are  there 
in  the  cistern  ? 


PRACTICAL  BUSINESS  MEASUREMENTS  133 

3.  A  cylindrical  tank  22  ft.  in  diameter  is  filled  with  water 
to  the  depth  of  18  ft.  What  is  the  weight  of  the  water  (1  cubic 
foot  of  water  weighs  62.5  lb.)  ? 

4.  A  man  contracted  to  dig  a  cistern  7  ft.  in  diameter,  24  ft. 
deep  at  the  rate  of  11.20  per  cu.  yd.     Find  the  entire  cost. 

5.  Find  the  cost  of  cementing  this  cistern  at  $  1.80  per  square 
yard. 

6.  How  many  yards  of  sheet  iron  will  be  required  for  a  smoke- 
stack 3  ft.  in  diameter  and  24  ft.  high,  allowing  1  in.  for  the  lap  ? 
What  will  be  the  cost  at  14  cents  per  square  foot  ? 

7.  If  a  steam  roller  is  5  ft.  high  and  7  ft.  long,  how  many  square 
feet  of  ground  will  it  roll  at  each  revolution  ? 

8.  At  7J  gal.  to  the  cubic  foot  what  will  be  the  capacity  of  a 
cylindrical  tank  having  a  base  of  6  ft.  and  an  altitude  of  14  ft.  ? 

9.  A  farmer  has  a  roller  2-|  ft.  in  diameter  and  6  ft.  wide. 
Allowing  4  in.  for  lapping,  how  far  must  the  team  travel  in 
rolling  a  rectangular  field  80  rd.  long  and  56  rd.  wide  ? 

10.  At  60  cents  a  square  yard  find  the  cost  of  polishing  a  cylin- 
drical monument  14  ft.  high  and  4  ft.  in  diameter. 

118.  The  sphere.  It  is  shown  in  geometry  that  the  number  of 
units  in  the  surface  of  a  sphere  is  equal  to  4:  ir  times  the  square  of  the 
number  of  units  in  the  radius;  and  the  number  of  units  in  the 
volume  of  a  sphere  is  equal  to  ^  tt  times  the  cube  of  the  number  of  units 
in  the  radius. 

Written  Work 

Find  the  surfaces  and  volumes  of  spheres  of  radii: 
1.    3'^  2.    1".  3.    2.5'^  4.    13'.  5.    24.2''. 

6.    8.24'.         7.    6.3".         8.    14.1'.  9.   8.7'.       lo.    12.3". 

11.  A  ball  with  a  radius  of  18  in.  is  to  be  gilded.  How  many 
square  inches  of  gilding  will  be  required  ? 

119.  Capacity.  Grain  is  usually  estimated  by  the  stricken  bushel 
of  2150.42  cu.  in.  ;  fruits,  vegetables,  coal,  and  corn  on  the  cob 
by  the  heaped  bushel  of  2747.71  cu.  in. 

Since  a  stricken  bushel  is  2150.42  cu.  in.,  and  there  are  1728 


134  PRACTICAL  BUSINESS  MEASUREMENTS 

1728 
cu.  in.  in  1  cu.  ft.,  therefore,  1  cu.  ft.  contains  -^prrTr-ri)  bushels 

or  approximately  .8  of  a  bushel. 

To  find  the  number  of  bushels  of  grain  a  bin  will  hold,  multiply  its 

capacity  in  cubic  feet  by  .8. 

1728 
A  cubic  foot  of  space  will  contain       ^       heaped  bushels,  or  .63 

heaped  bushels. 

To  find  the  number  of  heaped  bushels  that  a  bin  will  hold,  midtiply  its 

capacity  in  cubic  feet  by  .63.  ' 

Written  Work 

1.  How  many  bushels  of  potatoes  will  just  fill  a  bin  18'  x  7'  x  5'  ? 

2.  How  many  bushels  of  wheat  will  just-fill  a  bin  30'  x  &  X  6'? 

3.  A  wagon  bed  is  10'  long,  4'  wide,  and  2^'  deep.  How  many 
bushels  of  wheat  will  it  hold  ? 

4.  Mr.  Williams  wishes  to  build  a  bin  that  will  store  250  bushels 
of  wheat.  He  expects  to  make  the  bin  24'  long  and  6^'  wide. 
What  must  be  the  depth  ? 

5.  A  car  34'  long  and  7'  wide  is  filled  with  oats  to  a  depth  of 
4^'.     How  many  bushels  of  oats  are  in  the  car  ? 

A  gallon  is  equal  to  231  cu.  in.  A  cubic  foot  of  space,  there- 
fore, contains  -J-^^-  gallons,  or  7.48  gallons. 

To  find  the  number  of  gallons  when  the  cxibic  contents  may  be  founds 
multiply  the  capacity  in  cubic  feet  by  7.48. 

(^In  practice  1  cu.  ft.  is  considered  equal  in  capacity  to  7 J  gallons.) 

Written  Work 

Find  the  capacity  in  gallons,  of  : 

1.  A  cistern  12'  in  diameter  and  18'  deep. 

2.  A  tank  12'  long,  4^'  wide,  and  5'  deep. 

3.  A  cistern  14'  in  diameter  and  20.5'  deep. 

4.  What  is  the  capacity  in  gallons  of  a  cylindrical  tank  18.5' 
in  diameter  and  32'  deep  ? 

5.  A  cylindrical  standpipe  60'  high  has  a  diameter  of  14'. 
How  many  gallons  of  water  will  it  hold  ? 


PRACTICAL  BUSINESS  MEASUREMENTS  135 

120.  Board  Measure.  The  board  foot  is  the  unit  of  lumber 
measure.  It  is  a  board  1  ft.  long,  1  ft.  wide,  and  1  in.  thick. 
The  volume  of  a  board  foot  is  therefore,  144  cu.  in.  (except  when  the 
lumber  is  less  than  1  in.  in  thickness).  Boards  having  a  thickness 
of  less  than  1  in.  are  considered  as  having  a  thickness  of  an  inch. 

A  board  16  ft.  long,  12  in.  wide,  and  1  in.,  or  less,  in  thickness 
contains  16  board  feet.  If  the  thickness  were  IJ  in.,  the  board 
would  contain  24  board  feet. 

In  measuring  boards  that  taper  uniformly  the  average  width  is 
used. 

The  width  of  boards,  except  in  expensive  lumber,  is  generally 
taken  as  the  next  smaller  half  inch. 

When  no  thickness  is  mentioned  the  thickness  is  understood 
to  be  1  inch. 

It  should  be  evident  that  the  number  of  hoard  feet  is  the  product  of 
the  width  in  inches^  hy  the  thickness  in  inches^  by  the  length  in  feet^ 
by  the  number  of  pieces^  divided  by  12. 

Illustration     1.    How  many  board  feet  in  24  scantlings,  2"  x  4'', 

16'? 

24  X  2  X  4  X  16  ^  256,  the  number  of  board  feet. 
12 

Illustration    2.    How  many  board  feet  in  18  pieces,  each  ^"  x  9'', 

16'. 

18  x4x  9  X  16  ^  gg^^  ^j^^  number  of  board  feet. 

Oral  Work 

Compute  the  number  of  board  feet  in  each  of  the  following : 

1.  A  board  12  ft.  long,  1  ft. wide,  and  1  in.  thick. 

2.  A  board  7  ft.  lohg,  2  in.  wide,  and  1  in.  thick. 

3.  Two  boards  each  10  ft.  long,  4  in.  wide,  and  1  in.  thick. 

4.  Two  boards  each  14'  x  4"  x  12". 

5.  Twenty  boards  each  10'  x  3"  x  |'^ 

6.  One  hundred  boards  each  14'  x  4"  x  2". 

7.  Twenty-five  boards  each  9'  x  2"  x  1". 

8.  Three  hundred  boards  each  15'  x  4"  x  f ". 

9.  Fifty  boards  each  12'  x  6"  x  2". 


136 


PRACTICAL  BUSINESS  MEASUREMENTS 


Dealers  sometimes  use  a  table  in  determining  the  number  of 
board  feet  in  a  given  piece  of  timber.  A  portion  of  such  a  table 
is  given  below. 


Le>ngtu  in  Feet 

10 

12 

14 

16 

18 

2x4 

^ 

8 

n 

lOf 

12 

2x6 

10 

12 

14 

16 

18 

2x8 

m 

16 

18| 

21^ 

24 

2  X  10 

16f 

20 

23i 

26f 

30 

2  X  14 

231 

24 

32f 

37i 

42 

2^  X  12 

25 

30 

35 

40 

45 

2|  X  14 

29^ 

35 

40i 

46| 

52| 

3x6 

15 

18 

21 

24 

27 

3x8 

20 

24 

28 

32 

36 

Written  Work 

Determine  the  number  of  board  feet  in : 

1.  40  pieces  of  white  pine  2"  x  10^  18'. 

2.  130  joists  2"  X  8^  16^ 

3.  36  beams  4^'  x  8^  20. 

4.  20  planks  2^"  x  8^  18'. 

5.  80  joists  4."  X  4'',  20'. 

6.  At  $15  a  thousand,  find  the  cost  of  the  following : 

14  joists,  2''x    6'',  18' 

24  joists,  2"  X  10",  32'  . 

80  boards,         |"  x    4",  16' 

30  scantlings,  2"  x    4",  16' 

20  beams,         8"  x    9",  16'. 


CHAPTER   XIII 


Bed  Room 
ll'xl2' 


DRAWINGS   AND   GRAPHS 

Newspapers,  magazines,  and  trade  journals  make  frequent  use 
of  drawings  or  graphs  in  order  to  make  clear  the  relations  between 
magnitudes.  A  graph  will  often  reveal  a  relationship  much  more 
quickly  and  more  clearly  than  a  table  of  statistics. 

121.  Purposes  of  Drawings  and  Graphs.  Drawings  and  graphic 
representations  are  extensively  employed  for  two  purposes : 

a.    For  reference,  to  show  quickly  and  conveniently  the  shape 

and    dimensions   of    -^^__________^^^  

fields,  rooms,  build-    I  |  Q 

ings,  furniture,  ma- 
chinery, etc. 

Dimensional 
drawings  and  dia- 
grams, similar  to 
this  one,  are  of 
great  value.  An 
architect  designs  a 
building,  and  the 
contractor  builds  it 
in  accordance  with 
the  plan  shown  by 
the  drawing.  Tools 
and  machinery  are 
usually  constructed 
in  accordance  with 
drawings  prepared 
by  draftsmen  and 
designers. 

h.  To  present  sta- 
tistics in  a  manner 


Floor  Plan  of 
a  Bungalow 
Scale  ^=1'   . 


138 


DRAWINGS  AND  GRAPHS 


which  will  show  their  meaning  and  their  relationship  more  clearly 
than  can  be  done  by  columns  of  figures.  For  example,  the  rela- 
tive importance  of  Louisiana  as  a  producer  of  cane  sugar  is  made 
clearer  by  the  following  graph  than  by  the  table  of  statistics. 

Value  of  Cane  Sugar  Produced  in  Certain  States  in  1909 

State  Dollars 

Louisiana 17,752,537 

Georgia       2,268,110 

Texas 1,669,683 

Alabama 1,527,166 

Mississippi 1,506,887 

Florida 1,089,698 


Millions  of  Dollars 
12        3        4        5        6        7        8        9       10      11      12      13      14       15      16      17 

Louisiana 



^■"' 

^'^ 

"*" 

„^ 

^^ 

^^ 

""^ 



^^^ 



■"" 

Georgia 

"" — 

"^ 

" 

Texas 

Alabama 

^"* 

■" 

Mississippi 

*^" 

** 

Florida 

— 

122.  Drawing  to  Scale.  The  ability  to  read  drawings  and  graphic 
representations  intelligently  depends  somewhat  upon  a  knowledge 
of  how  to  draw  figures  to  scale. 

The  values  represented  by  the  lines  in  drawings  and  graphs  can 
be  easily  determined  because  the  lines  are  drawn  to  scale  ;  that  is, 
a  certain  distance  on  the  drawing  represents  a  specified  amount  of 
the  quantity  represented. 

In  the  floor  plan,  on  page  137,  one  foot  of  true  distance  is  repre- 
sented by  -^2  ^f  an  inch  plotted  distance  on  the  drawing.  All  lines 
in  the  drawing  correspond  to  this  scale. 

In  the  graph  showing  the  production  of  cane  sugar,  ^  inch 
represents  a  value  of  $  1,000,000. 

123.  Types  of  Scales.  The  scale  may  be  stated  in  various  ways, 
the  most  common  of  which  are  : 


DRAWINGS  AND  GRAPHS 


139 


a.    A  fraction. 

For   example,   a   scale   of   \  means  that  the  true  distances  or 
values  are  four  times  as  great  as  the  plotted  distances  or  values. 

h.  Statement  of  equivalent 
dimensions  or  values. 

For  example,  V^=V .  (Read 
1  in.  =  1  ft.)  One  inch  of 
the  drawing  represents  one 
foot  of  the  real  object.  In  the 
graph  showing  cane  sugar 
production  the  scale  is  f  = 
$1,000,000,  that  is,  |  inch  rep- 
resents 11,000,000. 

c.  A  diagram  or  scaled  rule 
accompanying  the  drawing. 
This  is  the  method  commonly 
used  in  map  drawing.  Thus, 
in  the  map  shown  here,  the 
scale  is  indicated. 


Scale  3U  Miles  to  1  loch 
5       10       15       20      25 


d.    The  graph  may  be  drawn  on  ruled  paper,  the  distance  be- 
tween the  ruled  lines  representing  a  specified  value. 


Exercise 

1.  A  scale  of  1''  =  l^  is  equivalent  to  what  fractional  scale  ? 

2.  A  scale  of  1^'  =  5'',  is  equivalent  to  what  fractional  scale  ? 

3.  A  scale  of  1^'  =  5^  is  equivalent  to  what  fractional  scale  ? 

4.  If  the  scale  is  J^^  what  distance  on  the  drawing  would  repre- 
sent 6'  3''?     4' 9^'? 

5.  If  the  scale  is  ^^,  what  plotted  distance  would  represent 
750  feet  ?     750  inches  ? 

6.  If  the  scale  is  1"  =  1000  bushels,  what  distance  on  a 
graph  would  represent  5125  bushels  ?  8500  bushels  ?  1750 
bushels  ? 


140 


DRAWINGS  AND  GRAPHS 


The  following  floor  plan  is  drawn  to  a  scale  of  Jg. 

7.  One  inch  of  plotted  dis- 
tance on  the  floor  plan  is  equiva- 
lent to  how  many  feet  of  true 
distance  ? 

8.  One  foot  of  true  distance 
on  the  floor  plan  is  represented 
by  what  part  of  an  inch  on  the 
drawing  ? 

9.  What  are  the  true  di- 
mensions of  this  room  ? 

10.    Assume  that  this  draw- 
ing is  made  to  the  scale,, |  in.= 
1  ft.  (y  =  1').      What  are  the  true  dimensions  of  the  room? 

11.  The  map  on  p.  139  is  drawn  to  the  scale  1'^  =  ?  miles. 

12.  ^' '  on  this  map  represents  what  true  distance  ? 

13.  What  is  the  true  distance  between  each  of  the  towns  on  the 
railroad  ?     Measure  distances  from  centers  of  towns. 

14.  An  electric  railroad  is  in  process  of  construction  between 
Morton  and  Harritown.  It  is  surveyed  in  a  direct  line.  How 
much  shorter  will  this  road  be  than  the  one  via  Sterling  ? 

15.  It  is  planned  to  locate  a  power  house  halfway  between 
Sterling  and  Harritown.  Indicate  its  position  on  the  map  and 
determine  its  distance  from  the  two  towns.  How  far  will  it  be 
from  the  nearest  point  on  the  new  electric  line  ? 

The  following  is  an  illustration  of  a  graph  drawn  on  ruled 
paper.  The  figures  along  the  top  of  the  graph  indicate  the  num- 
ber of  millions  of  bushels  of  wheat  grown.  Quantities  smaller 
than  10,000,000  bushels  can  be  approximated  with  sufficient  accu- 
racy for  general  comparative  purposes.  For  example,  the  wheat 
crop  of  1870  is  shown  by  the  graph  to  have  been  about  236,000,000 
bushels,  and  that  of  1904,  about  553,000,000  bushels. 


DRAWINGS  AND   GRAPHS 


141 


Millions  of  Bushels 
0    50   100   150  200   250   300   350   400   450   500   550   600   650   700   750 

1870 

1875 

1880 

1885 

1890 

1895 

1900 

1901 

1902 

1903 

1904 

1905 

1906 

1907 

1908 

1909 

1 

1910 

Oral  Work 

1.  What  was  the  approximate  crop  of  each  of  the  years  shown? 

2.  What  was  the  record  crop  shown  by  the  graph  ? 

124.  Determining  the  Scale.  When  a  drawing  or  a  graph  is  to 
be  made,  it  is  first  necessary  to  determine  the  scale.  The  scale  de- 
pends, in  general,  upon  three  things : 

a.    The  size  of  the  paper  to  be  used. 

h.    The  largest  dimension  to  be  shown  on  the  graph. 

e.    Convenience  in  showing  fractional  parts  of  the  scale. 


142  DRAWINGS  AND  GRAPHS 

Example.  A  room  is  15'  6"  long  by  10'  3"  wide.  What  scale 
should  be  used  to  show  a  diagram  of  this  room  on  a  sheet  of  paper 
8"  by  10",  leaving  a  margin  of  at  least  one  inch  around  the 
drawing? 

Solution.     The  largest  dimension  of  the  room  is  15'  6",  or  186". 

The  largest  dimension  of  the  paper  is  10  inches.  After  deducting  2  inches 
for  margins,  there  is  a  space  of  8"  available  for  the  drawing. 

The  largest  scale  possible,  therefore,  is  8"  represents  186". 

This  is  equivalent  to  a  scale  of  1"  =  2^1".     (How  was  this  determined?) 

For  convenience  in  showing  fractional  parts  of  a  foot,  it  will  be  better  to 
use  the  scale  of  1"  =  24". 


Written  '^ork 

1.  With  the  scale  1"  =  2',  what  length  lines  would  represent 
the  dimensions  of  the  room  15'  6"  xlO'  3"  ? 

2.  Use  this  scale  to  make  a  drawing  of  a  room  12'  G"  by  9'  9". 

3.  A  field  is  120  rods  by  80  rods.  Scale,  1"=1  rod.  How 
large  a  paper  is  needed  to  diagram  the  field,  leaving  a  margin  of 
2  inches  all  around?     Would  this  be  a  reasonable  scale  to  use  ? 

4.  If  a  scale  1  inch  =  20  rods  is  used,  what  size  paper  is  neces- 
sary in  order  to  diagram  this  field  and  leave  a  margin  of  one  inch 
on  all  sides  ? 

5.  What  is  the  largest  scale  that  could  be  used  to  plot  this 
field  on  a  paper  the  size  of  this  page,  leaving  margins  of  at 
least  I"  ? 

6.  It  is  desired  to  show  by  a  graph  the  imports  of  coffee  into 
various  countries  of  the  world.  The  year  chosen  is  1910.  The 
United  States  was  the  largest  importer,  with  an  importation  in 
round  numbers  of  804,000,000  pounds.  The  graph  is  to  be  placed 
on  paper  the  same  size  as  this  page,  with  the  same  margins.  How 
long  a  line  would  represent  100,000,000  bushels  ? 

7.  If  the  names  of  the  countries  require  one  inch,  the  scale 
might  be inch  =  100,000,000  bushels. 

8.  Draw  a  diagram  of  your  schoolroom,  entering  the  dimen- 
sions as  illustrated  in  the  drawing  on  page  137. 


VARIOUS  TYPES  OF  GRAPHS  143 

9.  Draw  a  diagram  of  a  room  in  your  home.  Do  not  enter 
the  dimensions  but  state  the  fractional  scale  used,  and  draw  all 
lines  very  carefully  in  accordance  with  this^  scale. 

Note  to  Teacher.  When  these  drawings  are  brought  to  class,  they  may  be 
exchanged,  and  the  students  required  to  compute  the  dimensions  in  accordance 
with  the  scale  stated.  * 

10.  Draw  a  line  graph  (similar  to  the  one  on  page  138)  to  ex- 
press the  following  statistics. 

Exports  of  Tea  from  Various  Countries  in  1910 

Country  Pounds 

British  India 258,000,000 

Ceylon 182,000,000 

China 207,000,000 

Dutch  East  Indies 33,000,000 

Formosa 24,000,000 

Japan 40,000,000 

Singapore 2,000,000 

Rule  the  paper  thus  : 

0   10   20   30   40   50   60   70   80   90   100  110 


Use  the  scale  j"  =  10  million  pounds.  (How  large  a  paper  will 
you  need?) 

Arrange  the  countries  so  that  the  longest  line  will  be  at  the 
top  and  the  shortest  at  the  bottom,  the  others  being  placed  in  the 
order  of  their  lengths. 


Various  Types  of  Graphs 

125.  Colored  and  Shaded  Graphs.  By  the  use  of  different  colors 
of  ink,  or  different  shadings,  comparisons  may  be  made  to  show 
increase,  decrease,  or  various  changes  in  statistics  from  year  to 
year. 


144 


DRAWINGS  AND  GRAPHS 


The  following  graph  shows  the  average  number  of  wage  earners 
employed  in  manufacturing  industries  in  1899  and  1909.  The 
graph  is  limited  to  the  ten  states  employing  the  largest  number  of 


men. 


Average  Number  of  Wage  Earners,  by  States:   1909  and  1899 1 


Oral  Work 

1.  By  referring  to  the  graph,  determine  the  approximate  num- 
ber of  wage  earners  in  each  state  in  1899  and  in  1909. 

2.  Which  state  shows  the  greatest  increase  in  the  number  of 
wage  earners  between  the  years  1899  and  1909  ? 

126.    The  Circle  is  frequently  used  for  graphic  purposes.     It  is 
particularly  valuable  because  it  shows  two  things  very  clearly  : 

a.  The  relation  of  each  magni- 
tude to  each  of  the  others. 

h.  The  relation  of  each  magni- 
tude to  the  sum  of  all. 

This  graph  shows  clearly  that 
the  states  of  the  Middle  Atlantic 
Division  produce  a  greater  value 
of  manufactured  articles  than  the 
states  of  any  other  division,  and 
that  they  produce  about  one  third 
of  the  entire  value  of  the  manu- 
factures of  the  country. 

The  scale  used  in  making  cir- 
cular graphs  is  based  on  the  degree.     If  the   circumference  of 


Value  of  Manufactured  Products  i 


1  Reprinted  by  permission  of  the  United  States  IBureau  of  the  Census,  Depart- 
ment of  Commerce. 


VARIOUS  TYPES  OF  GRAPHS  145 

a  circle  were  divided  into  360  equal  parts,  each  part  would  be  one 
degree  of  arc.  Degrees  may  be  measured  by  an  instrument  called 
a  protractor. 

The  method  of  locating  the  lines  in  a  circle  graph  may  be  ex- 
plained by  showing  how  the  apace  occupied  by  the  Middle  Atlantic 
section  was  determined. 

This  section  produces  .345  of 
the  total  value  of  manufactured 
products.  It  should,  therefore, 
occupy  .345  of  the  circle. 

.345  of  360°  is  124.2°. 

Points  as  nearly  as  possible 
124.2°  apart  are  marked  off  on  the  circumference  with  the  aid  of 
the  protractor,  and  lines  are  drawn  from  the  center  of  the  circle 
to  these  points  on  the  circumference. 

Written  Work 

1.  The  total  exports  of  coffee  from  all  the  countries  of  the  world 
in  1910  were  2,163,764,874  pounds.     Brazil  exported  1,286,217,168 

pounds  or of  the  world's  trade.     It  should  therefore  occupy 

what  part  of  a  circle  designed  to  show  the  coffee  exports  of  the 
world  ?     How  many  degrees  of  arc  ? 

2.  The  next  largest  exporter  was  the  Netherlands,  with 
173,823,451  pounds.  What  part  of  the  world's  supply  was  pro- 
vided by  this  country?  What  part  of  the  circle  should  represent 
the  amount  of  coffee  exports  of  the  Netherlands? 

3.  Five  departments  of  a  wholesale  store  produced  profits  as 
follows : 

Dept,  Profits 


I 

12165.00 

II 

3297.00 

III 

794.00 

IV 

1719.00 

V 

4625.00 

Prepare  a  circle  graph  showing  what  per  cent  of  the  entire 
profit  was  made  by  each  department. 


146 


DRAWINGS  AND  GRAPHS 


127.    Graphic  Pictures.     Another  kind  of  graph  frequently  used 
IS  illustrated  below : 

Workingmen's  Expenditures 


FOOD 


RLNT 


CLOTHING 


<5UND111L5  -  rUtLTLlGft>  INSUR/^MCfc^Hfc/^LTH--  CW  TWt* 

Food $385.82 

Rent 161.36 

Clothing 98.79 

Sundries 60.28 

Fuel  and  light 36.94 

Insurance 18.24 

Health 14.02 

Carfares ;    .     .  10.53 

From  The  Independent. 

These  figures  are  based  on  a  study  of  the  wages  of  a  number  of 
workingmen,  whose  average  annual  income  was  $749.83  and  whose 
average  annual  expenditure  was  $  735.98. 

128.  The  Graphic  Curve.  Graphs  drawn  on  cross-sectioned 
paper  are  especially  valuable  when  it  is  desired  to  show  the  varia- 
tion of  statistics  during  consecutive  intervals,  as  from  month  to 
month,  or  from  year  to  year.  The  divisions  on  the  vertical  line 
may  represent  multiples  of  some  unit  of  value  and  those  on  the 
horizontal  line  represent  various  intervals  of  time. 

The  following  graph  shows  the  variations  in  the  monthly  sales 
of  a  store  during  two  years.     The  unbroken  line 


VARIOUS  TYPES  OF  GRAPHS 


147 


indicates  the  sales  for  the  year  1914  and  represents  the  following 


statistics : 

Sales  for  January 

.     $1426.80 

Sales  for  July   .     .     . 

.     $1167.85 

February    . 

.        1638.80 

August   .     . 

.     .       1232.65 

March     .     . 

.       1526.75 

September  . 

.     .       1386.64 

April       .     . 

.       1246.70 

October  .     . 

.       1566.45 

May  .     .     . 

.       1147.10 

November  . 

1626.30 

June  .     .     . 

.       1060.50 

December   . 

.        1575.25 

It  is  sufficient  for  com- 
parative purposes  to 
show  the  approximate 
sales  in  dollars. 

129.  How  this  Graph 
is  Drawn.  An  unbroken 
line  represents  the  data 
for  1914.  A  point  was 
placed  on  the  January 
line  at  a  point  repre- 
senting approximately 
$1425.00.  A  second 
point  was  placed  on 
the  February  line  at  a 
point  representing  ap- 
proximately 11638.00. 
Other  points  were  prop- 
erly located  on  the  other 
lines,  and  an  unbroken 
line,  or  curve,  was  then 
drawn  connecting  all  the  points.  In  the  same  way  the  dotted  line 
was  drawn  to  represent  the  data  for  1915. 


1750 
1700 
1G50 
ICOO 
1550 
1500 
1450 
1400 
1350 
1300 
123.) 
1200 
1150 
UOO 
1050 

/ 

/ 

/ 
/ 
/ 

\ 
\ 

1 

''/ 

\  ■ 

\ 

\ 

1 
1 

1 

/ 

\ 

/ 

\ 

'^% 

1 

1 

/ 

\ 

/ 

\ 

\ 
I      \ 

/ 

/ 

/ 

\ 

\ 

4 

' 

/ 

\ 

V 

\ 

/ 

\ 

l\ 

\ 
\ 

/ 

\ 

\ 
\ 
\ 

1 

\ 

\ 
\ 

/ 
/ 
/ 

F 

\ 

/ 
/ 

/ 

\ 

1 

/ 

\ 

\ 

1 

Feb. 
Mar. 
Apr. 
May 
June 
July 
Aug. 
Sept. 
Oct. 

Nov. 
Dec. 

Exercise 
Study  the  graph  and  answer  the  following  questions : 
1.    Was  there  any  uniformity  of  trade  from  year  to  year? 


That 


is,  did  the  busy  and  the  dull  months  follow  in  about  the  same 
order  each  year? 


148 


DRAWINGS  AND  GRAPHS 


2.  As  a  rule,  during  what  seasons  did  this  store  have  the 
largest  trade  ? 

3.  What  was  its  "dullest"  month? 

4.  How  did  the  business  of  1915  compare  with  that  of 
1914? 

5.  About  how  many  more  dollars'  worth  of  goods  were  sold 
during  August,  1915,  than  during  August,  1914  ? 

6.  Estimate  the  sales  for  each  month  of  the  year  1914.  If  your 
answers  are  within  $2.00  of  the  correct  amount,  they  will  be 
accurate  enough  for  purposes  of  comparison. 

7.  Discuss  the  value  of  such  a  graph. 

130.    The  following  graph  shows  a  slightly  different  use  of  the 

curve.  The  curves  serve 
to  compare  the  grades 
given  by  three  teachers 
in  a  certain  school, 
showing  what  per  cent 
of  the  students  in  their 
classes  received  certain 
grades. 

This  graph  was  made 
in  the  following  man- 
ner: 

A  table  was  prepared 
showing  what  per  cent 
of  each  teacher's  stu- 
dents received  grades  be- 
tween 40  and  50,  50  and 
60,  etc. 

For  example  :  Eight 
students  of  teacher  A 
received  grades  60-70. 
This  was  16%  of  the 
students  in  A's  classes. 


m 
m 

; 

\ 

/ 
; 

v 

\ 

\ 

/ 
/ 

\ 

/ 
; 

\ 
1 
1 

; 

// 

\  \ 

/  ( 

/-- 
/ 
/ 

V 

>. 

'7 

> 

f 

\ 

r 

^^ 

// 

^ 

A' 

/ 

\\ 

s. 

0 

\ 

1 

1 
1 

:>-' 

v^ 

1 

1 
I 

'^ 

'  -v^ 

1 
1 
1 

y 

^ 

1 

1/ 

/ 

'L 

40-50       50-60       GO  -  70       70  -  cSO      80  -  90    90  - 

LOG 

VARIOUS  TYPES  OF  GRAPHS 


149 


Teacher  A 

Graub 

Teacher  A 

Geade 

No.  of  Students 

Per  Cent  of 
Total  Number 

No.  of  Students 

Per  Cent  of 
Total  Numbei- 

40-50 
50-60 
60-70 

2 
4 

8 

4 

8 
16 

70-80 
80-90 
90-100 

12   • 
16 

8 

24 

32 
16 

The  curve  for  Teacher  A  was  plotted  thus : 

On  the  horizontal  line  above  40-50,  a  point  was  placed  to 
indicate  4%. 

On  the  horizontal  line  above  50-60,  a  point  was  placed  to 
indicate  8  %,  etc. 

All  of  the  points  thus  located  to  represent  grades  given  by  A 
were  then  connected. 

Oral  Work 

Interpret  the  curves,  stating  what  per  cent  of  the  students  of 

each  teacher  received  the  grades  specified. 

\ 
Written  Review 

Use  paper  S'^"  by  11'^  or  larger,  for  the  following  graphs. 

1.  By  a  graph  similar  to  the  first  one  on  page  144,  show  the 
following  statistics  of  exports  from  the  United  States  to  the 
United  Kingdom.  Use  black  ink  for  the  data  of  1910;  red  ink 
for  those  of  1911. 


Cattle     .     . 
Bacon    .     . 
Hams     .     . 
Fresh  Beef 
Lard      .     . 
Leather 
Machinery 
Copper  .     . 
Paraffin  Wax 
Petroleum  . 
Tobacco 
Fish  .     .     . 


1910 


1911 


£  2,578,000 

£  3,056,000 

4,453,000 

5,067,000 

2,329,000 

2,712,000 

1,070,000 

397,000 

4,201,000 

4,014,000 

4,057,000 

3,828,000 

2,287,000 

2,894,000 

2,568,000 

3,027,000 

871,000 

617,000 

3,745,000 

3,370,000 

2,815,000 

3,278,000 

1,021,000 

702,000 

150 


DRAWINGS  AND  GRAPHS 


2.  Show  graphically  what  part  of  the  coinage  of  the  years  named 
in  the  following  table  was  gold,  what  part  silver,  and  what  part 
other  coin. 


Gold 

Silver 

Other  Coin 

1909 
1910 
1911 
1912 

88,776,908 

104,723,735 

56,176,822 

17,498,522 

8,087,852 
3,740,468 
6,457,301 
7,340,995 

1,756,389 
3,036,929 
3,156,726 
2,577,386 

3.  By  drawings  of  corn  stalks,  ears  of  corn,  corn  cribs,  or  any 
other  suitable  design,  graph  the  following  statistics  of  corn  crops 
in  the  United  States. 


Year 

Bushels 

Year 

Bushels 

1870 

1880 
1890 

1,094,000,000 
1,717,000,000 
1,489,000,000 

1900 
1910 

2,105,000,000 
2,886,000,000 

4.  By  a  graph  similar  to  the  illustration  of  monthly  sales 
(p.  147),  show  the  variation  in  the  wholesale  price  of  corn  per 
bushel  by  months  for  the  following  years. 


January  . 
February 
March 
April  .  . 
May  .  . 
June  .  . 
July  .  . 
August  . 
September 
October  . 
November 
December 


1910 


Cents 


62.3 

65.2 

65.9 

65.5 

63.5 

65.2 

66.2. 

67.2 

66.3 

61.1 

52.6 

48.8 


1911 


Cents 


1912 


Cents 


48.2 

62.2 

49.0 

64.6 

48.9 

66.6 

49.7 

71.1 

51.8 

79.4 

55.1 

82.5 

60.0 

81.1 

65.8 

79.3 

65.9 

77.6 

65.7 

70.2 

64.7 

58.4 

61.8 

48.7 

VARIOUS   TYPES  OF  GRAPHS  151 

5.  Show  by  a  graph  the  data  for  the  attendance  at  your  school 
for  a  school  year.     (The  principal  can  supply  the  data.) 

6.  Graph  the  temperatures  for  a  certain  hour  of  several  succes- 
sive days. 

7.  Make  a  graph  showing  your  progress  in  speed  and  accuracy 
in  addition,  subtraction,  multiplication,  and  division  for  a  given 
set  of  examples. 

8.  What  is  the  largest  scale  that  could  be  used  to  represent  a 
square  farm  of  160  acres  on  a  paper  18^'  by  20' ^  leaving  a  margin 
of  at  least  1''? 

9.  Two  cities  known  to  be  60  miles  apart  are  21  inches  apart  on 
a  map.     What  is  the  scale  of  the  map  ? 


PERCENTAGE 
CHAPTER  XIV 

PERCENTAGE 

131.  Relation  of  Percentage  to  Common  and  Decimal  Fractions. 
Percentage  is  the  process  of  computing  by  hundredths.  The 
symbol  %  stands  for  per  cent. 

15 

Thus,  15  %  means  — —  or  .15. 

8 
8  %  means  — —  or  .  08. 

300%  means  1^  or  3.00. 

^%  means  -~  or  .00 J  or  .005.    . 

2 

%%  means-|-  or  .00?. 
^  ^  100  ^ 

71 

TJ%  means -^  or  .07|  or  .075. 
^  100  ^ 


Oral  Work 

Express  each  of  the  following  as  a  common  fraction  and  as  a 
decimal  fraction: 

3.  19%  4.    24% 

7.  J-5-%  8.    200% 

11.  -,l^%  12.    16f% 

Express  with  the  symbol  % : 

13.    .74  '    14.    .03  15.  .07 J  16.    2.00 

17.    .32^  18.    .001  19.  1.00  20.    .OOJ.C 

152 


1.    7% 

2.    4% 

5.     2i  fo 

6.    i% 

9.    184% 

10.   5i% 

PERCENTAGE  153 

21.     .5  22.     .005  23.     .16|  24.     .14|- 

25.    I  26.     i  27.    I  28.    | 

29.    I  30.    f  31.     f  32.     1 

33.  40%  of  a  quantity  is  how  many  hundredths  of  it?  What 
fractional  part  of  it  ? 

34.  100  %  of  a  number  is  how  many  times  the  number  ? 

35.  300  %  of  a  number  is  how  many  times  the  number  ? 

36.  140  %  of  a  number  is  how  many  times  the  number  ? 

37.  2  times  a  number  is  what  per  cent  of  the  number  ? 

38.  5  times  a  number  is  what  per  cent  of  the  number  ? 

39.  What  part  of  a  number  is: 

20%  of  it?  12%  of  it?  13%  of  it? 

80%  of  it?  75%  of  it?  |^%ofit? 

100 %  of  it?  I  %  of  it  ?  121  %  of  it  ? 

37i%ofit?  871%  of  it?  50%  of  it? 

6|  %  of  it  ?  621  %  of  it  ?  66|  %  of  it  ? 

40.  Express  each  of  the  following  as  a  decimal  fraction  and 
with  the  symbol  %. 

1115321324       1        5       73 
2'   5'  ^'  6'  ■?'  T'  T'  2'   3'   5'   10'  T2''   8'  4* 

41.  The  following  table  states  the  fractional  part  of  the  total 
number  of  colonies  of  bees  in  the  United  States  owned  in  each 
section  of  the  country.  State  what  per  cent  of  the  colonies  are 
owned  in  each  section. 

New  England 012 

Middle  Atlantic 085 

East  North  Central 158 

West  North  Central 159 

South  Atlantic 197 

East  South  Central 147 

West  South  Central 11 

Mountain 05 

Pacific 082 


154  PERCENTAGE 

42.  The  following  table  shows  the  per  cent  of  the  total  value  of 
live  stock  owned  in  each  section  of  the  United  States.  State  these 
per  cents  as  decimal  fractions. 

New  England 2     % 

Middle  Atlantic 7.1  % 

East  North  Central 19.8  ^o 

West  North  Central 31.5% 

South  Atlantic lA^Jo 

East  South  Central 7.5  % 

West  South  Central .  12     % 

Mountain l.^^o 

Pacific.     .     .     .   ■ 4.8 9i, 

132.    Terms  Used  in  Percentage. 

Base.  The  number  of  which  a  given  per  cent  is  to  be  taken  is 
called  the  base. 

Rate.     The  per  cent  of  the  base  to  be  taken  is  called  the  rate. 

Percentage.  The  result  obtained  by  taking  a  certain  per  cent 
of  the  base  is  called  the  percentage.     Thus, 

64   X.25     =        16; 
or  base  x  rate  =  percentage. 

Fundamental  Processes  of  Percentage 
Computations  in  percentage  are  based  on  the  following : 
base  X  rate  =  percentage. 
64  x.25  =  16. 

Since  the  percentage  is  the  product  of  the  base  and  rate,  it  is 
evident  that, 

a.  The  percentage  divided  by  the  base  equals  the  rate.  For 
example  :  16  -^  64  =  .25  =  25  %. 

h.  The  percentage  divided  by  the  rate  equals  the  base.  For 
example  :  16  h-  25  %  =  16  -^  .25  =  64. 

From  these  statements  it  is  evident  that  if  any  two  of  the  terms 
are  known,  the  other  one  can  be  found. 

In  the  chapter  on  Decimal  Fractions  you  learned  how  to  multi- 
ply and  divide  by  any  number  expressed  decimally.     Percentage 


FUNDAMENTAL  PROCESSES  155 

involves  the  mathematical  principles  of  decimal  fractions.  The 
exercises  in  decimal  fractions  involved  computations  with  tenths, 
hundredths,  thousandths,  etc.  In  Percentage,  computation  is  by 
hundredths. 

All  mathematical  computations  involved  in  percentage  may  be 
grouped  under  three  headings: 

a.  To  find  a  given  per  cent  of  a  number. 

b.  To  find  what  per  cent  one  number  is  of  another. 

c.  To  find  a  number  when  a  certain  per  cent  of  it  is  known. 

133.    To  find  a  given  per  cent  of  a  number;   that  is,  to  find  the 
percentage. 

Examples.     1.    Find  1  %  of  428. 
Solution.     1  %  =  .01.     .01  of  428  =  4.28. 

2.  Find  7  %  of  378. 
Solution.     .07  x  378  =  26.46. 

3.  Find  14  %  of  8360. 

Solution.  $  300 

.14 
1440 
360 


$  50.40 
To  Ji7id  the  percentage,  multiply  the  base  by  the  rate. 

Oral  Work 

1.  Find  1  %  of  each  of  the  following:    18;    146;    198;    7; 
03;  876;  .045. 

2.  Find  5  %  of  each  of  the  following :  80  ;  60  ;  25  ;  42. 

3.  Find  10  %  of  $  18.20 ;  of  478  mi. ;  of  32  yd.  ;  of  648  A. 

4.  How  many  places  should  be  pointed  off  in  finding  each  of 
the  following: 

17%  of  4762?  17%  of  476.2?  17%  of  47.62? 

1.7  %  of  4762  ?  .17  %  of  4762  ?  17  %  of  .4762  ? 

5.    Find  10  %  of  400  :  560 ;  8.46. 


156  PERCENTAGE 

6.    Find  3%  of  40;  60;  15.  7.  Find  100  %  of  15 ;  40;  3. 

8.    Find  20  %  of  80  ;  70 ;  60.  9.  Find  50  %  of  40 ;  2 ;  10. 

10.    Find  30  %  of  30;  40;  80.        ll.   Find  12-i  %  of  480;  96;  640. 
12.    Find  371%  of  24;  80;  72.        13.   Find  200  %  of  9;  32;  181. 
14.    Find  14f  %  of  21;  35;  350.     15.   Find  25  %  of  12;  17;  96. 
16.    Find  j  %  of  120;  34;  18. 

Written  Work 
Find  : 

1.    17  %  of  472.  2.  92  %  of  $537.  3.  16f  %  of  1420. 

4.    3  %  of  48,729.        5.  200  %  of  37  ft.         6.   1.8  %  of  42,690. 

7.    17.5  %  of  479,362.  8.  250  %  of  il42. 

9.    128  %  of  346  yd.  lo.  5  %  of  83.6. 

11.    ^  %  of  42.736.  12.  1  %  of  8476. 

13.    32  %  of  14.76.  14.  19  ojo  of  .084. 

15.    25  ojo  of  264  sq.  mi.   ^  16.  371-  %  of  24  A. 

17.    121  oj^  of  1488.  18.  871  %  of  648  mi. 

19.    33J  %  of  \.  20.  20  ojo  of  |. 

21.    6f  %  of  32  cu.  ft.  22.  40  %  of  85  sq.  rd. 

23.    62J  %  of  40  A.  24.  33 J  %  of  $36. 

25.    66|  %  of  120  ft.  26.  Vl\  %  of  64  yd. 

27.  A  school  has  an  enrollment  of  450  students.  How  many 
students  are  absent  when  4  %  are  absent  ? 

28.  What  is  1 200  increased  by  4  %  of  itself  ? 

29.  In  1900  the  population  of  a  certain  city  was  52,840.  In 
1910  the  population  was  15  %  larger  than  in  1900.  What  was  the 
population  in  1910? 

30.  A  boy  made  a  journey  of  48  miles.  He  rode  85  %  of  the 
distance  in  an  automobile  and  walked  the  remaining  distance. 
How  far  did  he  walk  ? 

31.  An  architect's  fees  for  designing  a  house  are  4  %  of  its  cost. 
The  cost  is  $7360.     What  is  the  fee  ? 

32.  A  man  whose  salary  is  $3200  spends  19  %  of  it  for  rent. 
How  much  does  he  spend  for  rent  ? 


FUNDAMENTAL  PROCESSES 


157 


33.  A  clerk  receives  2  %  of  the  amount  of  his  sales.  If  his  sales 
for  Monday  were  1160.40,  how  much  did  he  receive  ? 

34.  The  report  of  a  school  with  an  attendance  of  400  showed 
the  per  cent  of  tardiness  to  be  1^.     How  many  were  tardy? 

35.  A  man  earns  il400  a  year  and  saves  18  %  of  it.  How  long 
will  it  take  him  to  save  i  756  ? 

36.  In  a  recent  year,  the  following  live  stock  was  reported  on 

farms  in  the  United  States :  numbkr 

Cattle 61,803,866 

Horses 18,833,113 

The  following  table  shows  the  per  cents  of  the  total  number  of 
cattle  and  horses,  in  terms  of  the  above  data,  in  each  section  of  the 
country.  Thus  5.2  %  of  61,803,866  was  the  number  of  cattle  in 
the  Pacific  States. 


Section 


New  England  .     . 
Middle  Atlantic    . 
East  North  Central 
West  North  Central 
South  Atlantic 
East  South  Central 
West  South  Central 
Mountain     .     .     . 
Pacific     .... 


Cattle 


HOESES 


2.2  <fo 

1.8% 

6.8 

6.2 

15.9 

22.2 

28.6 

34.3 

7.8 

5.6 

6.4 

5.8 

17.3 

11.8 

9.8 

7.2 

5.2 

5.1 

Rule  a  form  with  the  headings  suggested  below.  Enter  the 
facts  given  above ;  find  the  number  of  cattle  and  horses  in  eacli 
section  of  the  country  and  enter  the  statistics  on  the  blanks. 

Cattle  and  Horses  in  United  States 


{iXOTIOK 


Cattle 


United  States  Total 
61,803,860 


Per  Cent 


Number 


II0K8BS 


United  States  Total 
18,833,118 


Per  Cent 


Number 


158  .  PERCENTAGE 

134.    To  find  what  per  cent  one  number  is  of  another ;  that  is,  to 
find  the  rate. 

Method.     Since  the  percentage  is  the  product  of  the  base  and 
the  rate,  and  since  the  product  may  be  divided  by  one  factor  to 
determine  the  other  factor,  we  have  the  following : 
percentage  h-  base  =  rate. 

Examples.     1.    6  is  what  per  cent  of  12  ? 
Solution.  36^  =  1  =  .50  or  50  %. 

2.  A  farmer  had  72  sheep  and  sold  18  of   them.     What   per 
cent  of  his  flock  did  he  sell  ? 

Solution.  18  ^  72  =  .25  or  25  %. 

3.  George  had  one  brother  and  three  sisters.     What  per  cent 
of  the  children  were  boys  ? 

Solution.  There  were  5  children  in  the  family, 

f  of  the  children  were  boys. 
2  H-  5  =  .4  or  40  %. 

Oral   Work 

1.  What  per  cent  of  8  is  4? 

2.  What  per  cent  of  8  is  2  ? 

3.  What  per  cent  of  24  is  3  ? 

4.  What  per  cent  of  12  is  18  ? 

5.  What  per  cent  of  9  is  3? 

6.  What  per  cent  of  25  is  5? 

7.  What  per  cent  of  25  is  20  ? 

8.  What  per  cent  of  15  is  30  ? 

9.  What  per  cent  of  10  is  8  ? 

10.  What  per  cent  of  50  is  20  ? 

11.  What  per  cent  of  60  is  40  ? 

12.  15  is  what  per  cent  of  20  ? 

13.  20  is  what  per  cent  of  40  ? 

14.  18  is  what  per  cent  of  24  ? 

15.  1  ft.  is  what  per  cent  of  1  yd.? 

16.  20  bu.  are  what  per  cent  of  60  bu.? 


FUNDAMENTAL  PROCESSES  159 

17.  4  mo.  are  what  per  cent  of  1  yr.? 

18.  8  da.  are  what  per  cent  of  1  wk.? 

19.  .  If  you  sleep  8  hr.  out  of  24,  what  per  cent  of  the  time  do 
you  sleep  ? 

20.  If  a  man  earns  f  24  a  \Yeek  and  saves  $4,  what  per  cent  of 
his  earnings  does  he  save  ? 

21.  An  agent  sold  goods  amounting  to  11800  and  received  $200 
for  his  services.     What  per  cent  did  he  receive  on  the  sales  ? 

Written  Work 

1.  A  baseball  team  played  60  games  and  won  42.  What  per 
cent  of  the  games  played  did  the  team  win? 

2.  In  a  school  of  250  students  45  were  absent.  What  per  cent 
of  the  students  was  absent  ? 

3.  In  a  school  auditorium  there  are  650  seats.  Four  hundred 
eighty  of  the  seats  are  reserved  for  the  students.  What  per  cent 
of  the  seats  is  not  reserved  ? 

4.  A  building  worth  $14,500  is  insured  for  $10,150.  For 
what  per  cent  of  its  value  is  it  insured  ? 

5.  In  a  spelling  lesson  a  boy  spelled  all  but  4  of  the  30  words 
correctly.     What  per  cent  of  the  words  did  he  spell  correctly  ? 

6.  A  corporation  has  a  capital  stock  of  $  164,000.  Dunham  owns 
$41,000  of  the  stock.     What  per  cent  of  the  stock  does  he  own? 

7.  A  business  man  invested  $3000.  His  income  from  the  in- 
vestment the  first  year  was  $420.     What  per  cent  did  he  earn  ? 

8.  In  a  certain  school  there  are  224  boys  and  312  girls. 
What  per  cent  of  the  total  enrollment  is  boys  ?  girls  ? 

9.  Eighteen  of  the  boys  in  this  school  failed  to  pass  in  at 
least  one  study.     What  per  cent  of  the  boys  failed  ? 

10.  Twenty-three  of  the  girls  failed.  What  per  cent  of  the 
girls  failed? 

11.  What  per  cent  of  the  entire  school  failed  ? 

12.  In  1910,  the  total  population  of  the  United  States,  10  years 
of  age  and  over,  was  71,580,270.  Of  this  number,  5,517,608 
were  unable  to  either  read  or  write.  What  per  cent  of  the  popu- 
lation was  illiterate  ?  . 


160 


PERCENTAGE 


13.  The  total  population  of  the  United  States  in  1910  was 
91,972,266.  The  number  of  foreign-born  inhabitants  was 
13,345,545.  What  per  cent  of  the  total  population "  was  foreign 
born  ? 

14.  The  largest  number  of  foreign-born  people  were  Germans. 
They  numbered  2,501,181.  What  per  cent  of  the  entire  popu- 
lation was  of  German  birth  ? 

15.  What  per  cent  of  the  foreign-born  population  was  of 
German  birth? 

16.  The  forests  of  the  United  States  originally  contained  about 
5200  billion  board  feet  of  timber.  Cutting,  clearing,  and  fire  have 
reduced  the  stand  to  about  2500  billion  board  feet.  What  per 
cent  of  the  timber  remains  ? 

17.  The  following  table  is  similar  to  one  used  by  a  clothing 
store  to  determine  the  tailoring  firm  which  furnishes  suits  having 
the  best  sale.  Record  is  kept  of  the  number  of  suits  purchased 
from  each  firm,  and  of  the  number  of  these  suits  sold. 

Find  what  per  cent  of  the  suits  purchased  from  each  of  the 
manufacturers  was  sold,  and  enter  all  statistics  on  a  ruled  form 
similar  to  the  model. 

Of  what  value  is  this  table  of  statistics  to  the  merchant? 


Per  Cent  of  Sales  from  Stock  Purchased  from  Clothing 
Manufacturers 


MANUFACTUJfCJt 

NUMBCR 
BOVGHT 

HVMBER 
SOLD 

PER  CENT 
SOLD 

TAYLOR,  BJflCMT  &  CO 

3C8 

3.C73 

WCILS    ^  BAILEY 

V^^v3 

3  /^ 

r.HBA  INUM 

63C? 

^82 

Dl/DLrY&  COLC 

SZ3 

^/6 

W/LLIAMS,  CLDPlDCS  i,   CO. 

g  (,3 

^  /  q 

M.O  HARTMAN  &  SONS 

/  3>efa 

/  &0S, 

WC  DENNISTON  <S>  CO- 

/  OAO 

(fOsS- 

FUNDAMENTAL  PROCESSES 


161 


18.  The  following  table  shows  one  of  the  ways  in  which  mer- 
chants determine  which  clerk  is  selling  the  most  goods. 

Rule  a  form  similar  to  the  model ;  enter  on  the  blank  the 
facts  which  are  given  in  the  model ;  find  the  total  sales  made  by 
air  of  the  salesmen.  Find  what  per  cent  of  the  total  sales  was 
made  by  each  salesman.     Enter  all  of  these  facts  on  the  blank. 

Table  Showing  Per  Cent  of  Month'8  Sales  Made  by  Various  Salesmen 


SAirSMAJiriS  J^AME 

SALES 

PERCENT  or  TOTAL 

i/  B.Drf/MY 

/    / &6,iA 

■9^ 

O.F.ALBRIGHT 

/  Cf  /  3 

^s. 

G.r.SLATrji 

/  7S& 

c<^ 

WriLIAM.  WAJiXCR 

S-H  /3 

7^ 

C.B.WlLZr 

/  Cf  ^3 

¥^ 

H.  WALKER 

/  ^27 

3S. 

rRAXK  M'Grr 

/  6  q*& 

r  8 

r.L.MOUTGOMSJiY- 

&  /  Ji8 

¥-S 

C.H.HrURY 

/  7&S 

^4 

• 

TOTAL 

i 

,  19.  The  following  tabulation  is  a  record  of  a  week's  sales  in 
four  departments  of  a  store. 

Rule  a  blank  similar  to  the  model. 

Enter  the  statistics  on  the  blank. 

Find  the  total  sales  for  each  day  made  in  all  departments  ; 
enter  these  totals  in  the  "  total  "  column  at  the  right. 

Find  the  total  sales  made  during  the  week  in  each  department ; 
enter  these  totals  on  the  line  at  the  bottom  marked  "total." 

Find  (in  two  ways)  the  total  sales  made  in  all  of  the  depart- 
ments for  the  entire  week.  Enter  in  the  space  marked  Grand 
Total. 


162 


PERCENTAGE 


Find  what  per  cent  of  the  grand  total  sales  was  made  eatih 
day  ;  enter  these  per  cents  in  the  column  at  the  right. 

Find  what  per  cent  of  the  grand  total  sales  was  made  in  each 
department.  Enter  these  per  cents  on  the  line  at  the  bottom 
marked  per  cent. 

One  of  ■  the  qualities  which  a  business  man  desires  in  his 
employees  is  the  ability  to  follow  directions.  This  exercise  will 
give  you  an  opportunity  to  prove  your  ability  along  this  line. 
Get  a  clear  understanding  of  the  instructions,  and  follow  them  by 
preparing  the  exercise  without  asking  for  any  further  directions. 

A  Week's  Sales  in  a  Department  Store 


Day 

Dept.  1 

Dept.  II 

Dept.  Ill 

Deft.  IV 

Total 

Per  Cent 

Monday   .... 

$362 

50 

$562 

83 

1862 

94 

$126 

39 

$ 

Tuesday  .... 

415 

75 

475 

92 

732 

83 

143 

62 

Wednesday  .     .     . 

896 

21 

415 

60 

769 

42 

129 

38 

Thursday      .     .     • 

472 

96 

516 

29 

640 

20 

145 

17 

Friday     .... 

387 

29 

429 

36 

721 

32 

96 

27 

Saturday.     .     .     . 

493 

89 

562 

64 

816 

25 

163 

92 

Total    .... 

Grand 
Total 

Per  Cent   .     .     . 

135.  To  find  a  number  when  a  certain  per  cent  of  it  is  known; 
that  is,  to  find  the  base. 

Method.  Since  the  percentage  is  the  product  of  two  factors,  the 
base  and  the  rate,  and  since  any  product  can  be  divided  by  one  of 
its  factors  to  find  the  other  factor,  it  is  evident  that, 

percentage  -^  rate  =  base. 

Therefore,  to  find  the  base,  divide  the  percentage  hy  the  rate  ex- 
pressed as  a  decimal. 

Examples.     1.    18  is  25%  of  what  number? 

Solution.     18  is  the  percentage,  25%  is  the  rate;  the  base  is  not  known. 
18  -f-  .25  =  the  required  number,  or  base. 
•      18  H-  .25  =  72. 


FUNDAMENTAL  PROCESSES  163 

2.    45  %  of  the  number  of  students  in  a  school  are  boys.     If  there 
are  135  boys,  how  many  students  are  in  the  school  ? 

Solution.     135  -=-  .45  =  300,  the  total  number  of  students. 

This  may  be  explained  as  follows  : 

Since  45  %  of  the  number  of  students  =  135, 

1  %  of  the  number  of  students  =  ^^  of  135  =  3 
and  100  %  of  the  number  of  students  =  100  x  3  =  300. 


Oral  Work 

Find  the  number 

of  wliich : 

1.    40  is  20%. 

2.    12  is  4%. 

3. 

10  is  5%. 

4.    86  is  2%. 

5.    f45  is  15%. 

6. 

40  is  80%. 

7.    12is|%. 

8.    42  is  100%. 

9. 

60  is  200% 

10.    12  is  33 J  %. 

11.    35  is  7%. 

12. 

19is  J%. 

13.    8  is  1%. 

14.    2700  is  66J%. 

15.  A  boy  lost  40  cents,  which  was  10  %  of  what  he  had.     How 
much  did  he  have? 

16.  A  man  sold  32  acres  of  land,  which  was  80  %  of  all  that  he 
owned.     How  many  acres  did  he  own? 

Written  Work 

1.  In  a  certain  school  5  %  of  the  pupils  are  absent  and  475 
pupils  are  present.     What  is  the  enrollment? 

2.  By  saving  28%  of  his  salary  a  man  saved  $2240  in  5  years. 
What  was  his  salary  ? 

3.  18.75%  of  a  class  failed.  If  26  passed,  how  many  were  in 
the  class  ? 

4.  The  distance  from  New  York  to  San  Francisco  via  the 
Panama  Canal  is  5278  miles.  This  distance  is  60.44  %  less  than 
the  distance  via  Cape  Horn.  What  is  the  distance  via  Cape 
Horn  ? 

5.  A  boy  paid  f3  for  a  pair  of  shoes  and  had  70%  of  his 
money  left.     How  much  money  had  he  at  first  ? 

6.  P^our  partners  engage  in  business.  The  first  invests  $4000; 
the  second  invests  $3000;  each  of  the  others  invests  25%  of  the 
total  capital.     What  is  the  total  capital  ? 


164  PERCENTAGE 

7.  The  Washington  Monument  is  555  ft.  and  Eiffel  Tower  is 
984  ft.  high.  The  height  of  the  monument  is  what  per  cent  of 
the  height  of  the  tower? 

8.  The  average  velocity  of  wind  is  18  mi.  per  hour  and  that 
of  sound  is  1090  ft.  per  second.  The  velocity  of  wind  is  what 
per  cent  of  the  velocity  of  sound  ? 

9.  The  mean  annual  rainfall  in  Denver  is  14  inches,  and  that  in 
New  York  City  is  44.8  inches.     Each  is  what  per  cent  of  the  other  ? 

10.  The  length  of  the  Hudson  River  is  280  miles ;  the  length 
of  the  Ohio  is  950  miles ;  and  the  length  of  the  Mississippi  is 
3160  miles.  The  length  of  each  is  what  per  cent  of  the  length  of 
the  others  ? 

11.  The  record  for  the  100-yard  dash  is  now  9|  sec.  It  was 
formerly  9|-  sec.     By  what  per  cent  was  the  record  reduced  ? 

12.  In  1776  there  were  13  states  in  the  Union.  There  are  now 
48  states.     What  has  been  the  per  cent  of  increase  ? 

13.  A  certain  basketball  player  can  shoot  on  an  average  90%  of 
his  free  chances.  If  there  are  20  fouls  called  on  his  opponents  in 
a  game,  how  many  points  should  he  make  on  fouls  ? 

14.  The  United  States  Census  divides  persons  engaged  in  manu- 
facturing into  three  classes  :  wage  earners,  clerks,  and  proprietors. 

The  table  on  page  165  shows  the  number  of  persons  in  the  first 
class;  that  is,  the  wage  earners.  It  also  shows  the  per  cent  of 
the  total  number  engaged  in  each  line  of  manufacturing  who  were 
wage  earners. 

For  example,  there  were  50,551  wage  earners  engaged  in  the 
manufacture  of  agricultural  implements.  The  wage  earners  were 
83.9%  of  the  total  number  of  persons  engaged  in  this  work. 
What  was  the  total  number  of  persons  engaged  in  this  work  ? 

Rule  a  form  and  find  the  total  number  of  persons  engaged  in 
such  industries  as  the  teacher  directs. 

Since  the  per  cents  are  only  approximate,  the  results  will  be 
only  approximate. 

Indicate  the  ten  industries  having  the  largest  number  of 
employees.  Mark  the  industry  with  the  largest  number  of 
employees  "  1,"  the  second  largest  "  2,"  etc. 


FUNDAMENTAL  PROCESSES 


165 


Industry 


Wage  Earners 
Av.  Number 

Per  Cent 

Total 
Employees 

Rank 

6,615,046 

86.1 

50,551 

83.9 

75,721 

88.7 

198,297 

91.8 

40,618 

89.4 

100,216 

69.4 

18,431 

58.5 

59,968 

83.3 

69,928 

84.3 

282,174 

93.7 

43,086 

91.5 

23,714 

85.3 

239,696 

88.3 

153,743 

85.9 

44,638 

81.4 

73,615 

84.7 

378,880 

97.7 

87,256 

82.6 

39,453 

59.7 

531,011 

86.3 

128,452 

89.1 

37,215 

73.0 

129,275 

94.9 

38,429 

89.2 

240,076 

92.1 

34,907 

80.2 

62,202 

92.7 

6,430 

77.2 

54,579 

81.8 

695,019 

88.5 

65,603 

84.9 

17,071 

80.2 

14,240 

65.0 

75,978 

93.3 

22,895 

55.7 

13,929 

8.37 

258,434 

66.5 

99,037 

94.1 

89,728 

82.5 

15,628 

92.8 

7,424 

92.1 

13,526 

86.4 

166,810 

84.4 

168,722 

96.3 

1,648,441 

86.0 

All  Industries 
Agricultural  Implements    . 

Automobiles 

Boots  and  Shoes  .... 
Brass  and  Bronze  .  .  . 
Bread      

Butter,  Cheese      .... 

Canning 

Carriages 

Cars  and  Shop  Construction 
Cars,  Steam 

Chemicals 

Clothing,  men's  .... 
Clothing,  women's  .  .  . 
Confectionery  .... 
Copper,  Tin 

Cotton  Goods 

Electrical  Machinery     .     . 

Flour  Mill . 

Foundry 

Furniture 

Gas 

Hosiery 

Iron,  Steel,  Blast  .  .  . 
I.  and  S.  Steel  Works  .  . 
Leather  Goods      .... 

Leather 

Liquors,  Distilled      .     .     . 

Liquors,  Malt 

Lumber 

Marble 

Oil 

Paint  and  Varnish    .     .     . 

Paper 

Patent  Medicines  .  .  . 
Petroleum 

Printing  and  Publishing     . 

Silk 

Slaughtering 

Smelting,  Copper  .  .  . 
Smelting,  Lead  .... 
Sugar  and  Molasses .  .  . 
Tobacco  Manufacture  .  . 
Woolen,  Worsted .... 
All  Other  Industries      .     . 


166  PERCENTAGE 

Percentage  of  Increase  and  Decrease 

Percentage  is  frequently  employed  to  find  the  relation  between 
numbers,  or  to  find  how  much  larger  or  smaller  one  number  is 
than  another.  This  does  not  involve  any  new  mathematical 
principles. 

Example.     What  number  increased  by  20  %.  of  itself  is  360? 

Solution.  100  %  of  the  number  =  the  number, 

20  %  of  the  number  =  the  increase, 
120  %  of  the  number  =  360, 

1  %  of  the  number  =  360  --  120  =  3, 
100%  of  the  number  =  100  x  3  =  300, 
or  we  may  say  :  1.20  times  the  number  =360,  therefore  the  number  =  ;J-—  =300. 

Oral  Work 
(Use  equivalent  fractions  if  more  convenient.) 
What  number  increased  by 

1.    20  %  of  itself  is  240?  2.  25  %  of  itself  is  250? 

3.    121  cf^  of  itself  is  360?  4.  200  %  of  itself  is  1800? 

5.    142  ^^  of  itself  is  88  ?  6.  75  %  of  itself  is  14? 

7.    50  %  of  itself  is  600?  8.  5  %  of  itself  is  420? 

9.    300  %  of  itself  is  2400?  lo.  87  J  %  of  itself  is  330? 

11.    1  %  of  itself  is  202?  12.  7  %  of  itself  is  428? 

13.    6|  %  of  itself  is  4800?  14.  661  %  of  itself  is  40? 

15.    60  %  of  itself  is  64?  16.  100  %  of  itself  is  600? 

17.  How  much  is  1^40  increased  by  20  %  of  itself? 

18.  How  much  is  60  increased  by  10  %  of  itself? 

19.  How  much  is  $42  increased  by  10%  of  itself? 

20.  How  much  is  3  increased  by  100  %  of  itself  ? 

21.  How  much  is  24  bu.  increased  by  37^%  of  itself? 

22.  How  much  is  12  yd.  increased  by  33J%  of  itself? 

23.  How  much  is  10  mi.  increased  by  7  %  of  itself? 

24.  How  much  is  -118  increased  by  200%  of  itself? 

25.  How  much  is  32  acres  increased  by  12^%  of  itself? 


INCREASE    AND    DECREASE  167 

136.    Per  Cent  of  Increase. . 

To  find  the  increase,  multiply  the  base  by  the  per  eeyit  of 
increase. 

Example.  Mr.  Smith,  whose  salary  was  1)1200.00,  received  a 
5%  increase.     How  much  was  the  increase? 

Solution.  $  1200    Base 

.Qd 

1 60.00     Increase 

To  find  the  per  cent  of  increase,  divide  the  increase  by  the  base. 
Example.     Mr.  Smith,  whose  salary  was  #1200.00,  received  an 
increase  of  $60.00.      What  was  the  per  cent  of  increase  ? 

Solution.  $  60.00  -  $  1200.00  =  .06,  or  5  %. 

To  find  the  base. 

a.  Given  the  increase  and  per  cent  of  increase. 

Example.  Mr.  Smith  received  a  5%  increase  in  salary.  The 
increase  was  160.00.     What  was  his  original  salary  ? 

Solution.  $60.00  -  .05  =  $  1200.00. 

Increase  -f-  per  cent  of  increase  =  base. 

b.  Given  the  increase  and  the  amount. 

Example.  Mr.  Smith's  salary  was  increased  f60.00,  after 
which  he  received  $1260.00.  What  was  the  per  cent  of 
increase  ? 

Solution.  $  1260  -  $  60  =  $  1200,  the  base. 

$60-^^1200  =  .05. 
Hence,  the  per  cent  of  increase  is  5  %. 

c.  Given  the  per  cent  of  increase  and  the  amount. 

Example.  After  receiving  a  5  %  increase,  Mr.  Smith's  salary 
was  $1260.00.  What  was  his  original  salary  and  what  was  the 
increase  ^ 

Solution.  His  original  salary  was  100%  of  itself.  His  increase  was  5% 
of  the  original  salary.     Therefore,  the  new  salary  was  105  %  of  the  old  one. 

$  1260  H- 1.05  =  $1200. 


168  PERCENTAGE 

Written  Work 

1.  A  merchant's  sales  during  1914  were  i  6238. 92.  By  adver- 
tising, he  increased  his  sales  f  2485.35  the  following  year.  What 
was  the  per  cent  of  increase,  and  what  was  the  amount  of  the 
jales  in  1915  ? 

2.  The  deposits  of  the  Wells  Street  Bank  on  June  30,  1914, 
were  $365,894.56.  On  June  30,  1915,  the  deposits  had  increased 
to  1396,268.55.  What  was  the  increase  and  the  per  cent  of 
increase  ? 

3.  A  factory  produced  240  articles  of  a  certain  kind  per 
day.  By  installing  new  machinery,  the  output  was  increased 
12|-%.  What  was  the  amount  of  the  increase,  and  how  many 
articles  were  produced  per  day  after  the  new  machinery  was 
installed  ? 

4.  Williams  paid  $16.87  more  taxes  this  year  than  he  did  last 
year;  an  increase  of  7.8%.  What  was  the  amount  of  his  taxes 
each  year  ? 

5.  The  payroll  of  the  Maynard  Manufacturing  Company  for 
the  week  ending  April  4, 1914,  was  $428.62.  The  payroll  for  the 
week  ending  April  3,  1915,  was  13  %  larger.  What  was  the  pay 
roll  for  the  week  in  1915,  and  what  was  the  increase  ? 

6.  A  merchant  built  an  addition  to  his  store  which  increased  the 
floor  space  28%.  After  the  addition  was  completed,  the  floor 
space  was  1280  square  feet.  What  was  the  number  of  square 
feet  of  floor  space  in  the  original  store,  and  what  was  the  amount 
of  the  addition  ? 

137.    Per  Cent  of  Decrease. 

To  find  the  per  cent  of  decrease,  divide  the  decrease  hy  the  base. 

Example.     Mr.  Smith's  coal  bill  in  1914  was  $80.00.     In  1915 
his  bill  was  $4.00  less.     What  was  the  per  cent  of  decrease  ? 
Solution.  Decrease  -r-  base  =  per  cent  of  decrease. 

Thus,  $4.00  -^  %  80.00  =  5  %. 
The  decrease  was  5  %. 


INCREASE  AND  DECREASE  169 

Written  Work 

1.  The  proprietor  of  a  retail  grocery  employed  five  clerks 
at  a  total  annual  expense  for  wages  of  $5000.00.  In  order  to 
reduce  the  expense,  he  released  one  clerk  whose  wages  were 
i  60.00  per  month.  How  much  did  he  decrease  the  cost  of  the 
clerk  hire  per  year  ?  What  was  the  per  cent  of  decrease  ?  What 
was  the  annual  cost  of  the  clerk  hire  after  one  clerk  was 
dismissed  ? 

2.  A  paper  mill  which  burned  2400  tons  of  soft  coal  per 
year  remodeled  its  furnaces  and  boilers  and  now  burns  2000 
tons  of  coal  per  year.  How  many  tons  less  does  this  factory 
consume  per  year  than  formerly,  and  what  is  the  per  cent  of 
decrease  ? 

3.  Previous  to  1914,  Mr.  Waterbury  owned  the  only  drug  store 
in  the  town  of  X.  When  a  new  drug  store  was  opened,  the  com- 
petition decreased  Mr.  Waterbury 's  annual  sales  -11067.60,  or 
17%.  What  was  the  amount  of  Mr.  Waterbury 's  sales  the  year 
before  the  new  store  opened  ? 

4.  In  1914  Mr.  Snowden,  a  grocer,  lost  1327.00  from  bad 
debts.  A  credit-rating  association  was  formed  in  the  town; 
the  merchants  informed  each  other  of  persons  who  did  not  pay 
their  bills;  and  the  following  year  Mr.  Snowden  decreased  his 
loss  from  bad  debts  18%.  How  much  did  the  credit-rating 
association  save  Mr.  Snowden,  and  what  was  his  loss  from  bad 
debts  in  1915  ? 

5.  Ratlibun  moved  his  store  into  a  new  building  where  the 
rent  was  15.00  per  month  less  than  the  rent  of  the  building 
which  he  formerly  occupied.  The  rent  in  the  new  location  was 
$125.00  per  month.     What  was  the  per  cent  saved? 

6.  Barnes  said  to  his  partner,  "  We  cut  down  our  delivery 
expense  30  %  when  we  sold  the  horses  and  bought  an  auto  truck. 
Our  annual  cost  for  making  deliveries  after  we  made  the  change 
was  only  11645.00.  When  we  delivered  with  horses,  the  cost  per 
year  was  $ ,  so  we  are  saving  | ." 


170 


PERCENTAGE 


7.  The  following  table  shows  one  of  the  uses  which  business 
men  make  of  per  cent  of  increase  and  decrease. 

This  table  compares  the  sales  on  the  first  Tuesday  in  June,  1914, 
with  the  sales  on  the  first  Tuesday  in  June,  1915.  The  merchant 
assumes  that  trade  conditions  were  about  the  same  on  the  two  days. 
A  table  of  this  kind  is  prepared  every  day,  comparing  the  business 
for  the  day  with  the  business  of  the  corresponding  day  of  the 
previous  year. 

Prepare  a  table  similar  to  the  model,  and  enter  the  facts  given. 
Show  increases  and  per  cents  of  increase  in  black  ink;  decreases 
and  per  cents  of  decrease  in  red  ink. 

What  was  the  increase  in  business  in  department  1  ?  What 
was  the  per  cent  of  increase  ? 

Complete  the  table. 

Comparative  Sales  Sheet 


Department 
Number 

Sales,  Tuesday, 
June  2,  1914 

Sales,  Tuesday, 
June  1,  1915 

Increase  or 
Decrease 

Per  Cent 

Increase  or 

Decrease 

1 

2 

1  826 
1034 

95 

78 

$   914 
1231 

32 
64 

1 

3 

1237 

62 

1196 

14 

4 

2643 

80 

2843 

27 

5 

1413 

80 

1376 

29 

6 

962 

40 

1235 

96 

7 

2642 

16 

2927 

92 

8 

1964 

39 

2129 

80 

9 

1636 

48 

1596 

27 

10 

1213 

42 

1723 

96 

11 

1394 

29 

1146 

92 

12 

415 

75 

496 

25 

13 

3460 

00 

3246 

29 

14 

2690 

70 

2889 

00 

15 

878 

25 

794 

60 

Total 

8.  The  following  table  shows  the  value  of  irrigating  arid  land. 
For  example,  the  government  records  show  that,  in  the  regions 
where   rainfall   is   insufficient,    the    potato    crop   on   an   acre   of 


INCREASE  AND  DECREASE 


171 


irrigated  land  is  worth  $15.37  more  than  the  crop  grown  on  an 
acre  of  unirrigated  land.     This  is  an  increase  of  34.4%  due  to 
irrigation.     What   is   the    average  value  per  acre  of  the  potato 
crops  grown  on  unirrigated  land  and  on  irrigated  land  ? 
Complete  the  table. 

Comparative  Value  of  Crops  Grown  on  Irrigated  and 
Unirrigated  Land 


Crop 


Potatoes 

Sugar  Beets 

Wheat 

Alfalfa 

Oats 

Barley 

Corn 

Timothy  and  Clover,  mixed 
Timothy  alone      .... 


Excess  of  Ayeragk  Value 
OF  Crop  per  Acre  grown 
ox  Irrigated  Land,  over 

THAT   GROWN    ON    UNIRRI- 
GATED Land 


$15 
5 
8 
5 
7 
6 
3 
3 
3 


34.4  % 

10.4 

58.6 

35.2 

63.2 

55.1 

24.0 

27.6 

24.1 


AVRBAGB  VaLXTE 

OF  Crop  per 
Acre  on  Unir- 
rigated Land 


Average  Value 

OF  Crop  per 

Acre  on 

Irrigated  Land 


138.  Per  Cent  of  Maximum.  It  is  sometimes  desired  to  com- 
pare a  certain  number  with  a  larger  number.  For  example,  a 
certain  packing  plant  is  equipped  to  slaughter  and  pack  a  maxi- 
mum of  2000  hogs  daily.  On  October  22,  this  plant  packed  1882 
hogs. 

The  day's  pack  was  Jiff  of  the  maximum  capacity,  or  91.6  %. 
State  a  rule  for  finding  per  cent  of  maximum. 


Written  Work 

The  table  on  page  172  shows  the  number  of  wage  earners  em- 
ployed in  coal  mining  in  the  United  States  in  a  recent  year.  The 
number  of  employees  varies  with  the  season.  Some  idea  of  the 
steadiness  of  employment  in  this  industry  may  be  formed  by 
comparing  the  number  of  employees  each  month  with  the 
maximum. 


172 


PERCENTAGE 


During   what   month   was   the  maximum   number   of   persons 
employed  in  coal  mining  ? 

What  per  cent  of  this  number  was  employed  in  January  ? 
Complete  the  table. 

Wage  Earners  Employed  in  Coal  Mining  in  the  United  States 


Month 


January 
February 
March    . 
April 
May  .     . 
June  .     . 
July  .     . 
August  . 
September 
October  . 
November 
December 


Wage  Earners 
Employed 


691,244 
686,322 
679,791 
649,870 
646,592 
652,894 
659,434 
667,146 
685,234 
704,939 
720,341 
729,273 


Per  Cent  of  Maximum 


139.  Per  Cent  of  Average.  Percentage  is  also  used  to  show  the 
relation  between  different  numbers  by  comparing  them  with  their 
average. 

Written  Work 

The  following  table  shows  the  monthly  sales  of  a  number  of 
clerks : 


Clerk  No. 

Sales 

Per  Cent 

Clerk  No. 

Sales 

Per  Cent 

201 
202 
203 
204 

$1412.32 

1218.16 

967.32 

1046.89 

205 
206 
207 

208 

$1836.24 
1216.26 
1375.85 
1493.85 

Find  the  average  sales. 

The  sales  of  Clerk  No.  201  are  what  per  cent  of  the  average  ? 

Complete  the  table. 

What  is  the  value  of  such  a  table  for  the  manager  of  a  business  ? 


INCREASE  AND  DECREASE 


173 


Review  Work 

1.  If  a  merchant  sells  all  goods  at  an  advance  of  10  %  of  the 
cost,  what  will  be  the  selling  price  of  an  article  which  cost  $  3.40  ? 
What  will  be  the  profit  on  this  article  ?  If  this  merchant's  an- 
nual sales  are  $  24,126.85,  what  is  his  gross  profit  ? 

He  marked  all  goods  at  25  %  increase  on  the  cost  the  following 
year  and  his  sales  dropped  to  f  15,625.90.  What  was  the  cost  of 
the  goods  sold,  and  the  gross  profit  ? 

2.  In  1910  the  total  area  of  the  Indian  reservations  in  the 
United  States,  exclusive  of  Alaska,  was  77,446  square  miles.  In 
1890  the  area  of  such  reservations  was  243,991  square  miles.  What 
per  cent  did  the  area  decrease  in  twenty  years  ? 

3.  In  1910  the  Indian  population  was  300,121,  in  1890  it  was 
243,524.     What  per  cent  did  the  population  increase  ? 

4.  What  was  the  average  number  of  acres  of  land  in  reserva- 
tions per  Indian  for  each  of  the  years  named  ? 

5.  What  was  the  per  cent  of  increase  or  decrease  in  the  average 
acreage  ? 

6.  Complete  the  following  table  showing  the  average  size  of 
farms  in  different  divisions  of  the  country. 


Division 

Average  Size  op  Fabms 
(Acres) 

Increase  (+) 
Decrease  (-) 

1910 

1900 

Acres 

Per  Cent 

United  States     .     . 
New  England     .     . 
Middle  Atlantic 
East  North  Central 
West  North  Central 
South  Atlantic  .     . 
East  South  Central 
West  South  Central 
Mountain       .... 
Pacific.     .... 

138.1 

104.4 

92.2 

105.0 

209.6 

93.3 

78.2 

179.3 

324.5 

270.3 

146.2 
107.1 

92.4 
102.4 
189.5 
108.4 

89.9 
233.8 
457.9 
334.8 

174  PERCENTAGE 

7.  The  following  table  shows  the  amount  of  sugar  produced  in 
and  imported  to  the  United  States.     Complete  the  table. 

Long  Tons 
,      (2240  LB.) 

Sugar  imported  from  Hawaii  and  Porto  Rico   ....        718,788 

Sugar  imported  from  other  countries 1,674,776 

Total  imports x,xxx,xxx 

Domestic  production  of  cane  sugar 409,960 

Domestic  production  of  beet  sugar 434,000 

Total  domestic  production x,xxx,xxx 

Total  consumption  of  sugar  in  United  States      .     .  x,xxx,xxx 

a.  What  per  cent  of  the  total  consumption  of  sugar  was  imported  ? 

b.  What  per  cent  of  the  sugar  consumed  was  produced  in  this 
country  ? 

c.  What  per  cent  of  the  sugar  made  in  this  country  was  cane 
sugar  ?     What  per  cent  was  beet  sugar  ? 

8.  Complete  the  following  table. 


Pkrsons  Engaged  in  Manufactures 

Glass 

1904 

1909 

Per  Cent  of 

Number 

Per  Cent 
of  Total 

Number 

Per  Cent 
of  Total 

Increase, 
1904-1909 

Proprietors  and  firm  members 
Salaried  employees     .... 
Wage  earners  (average  number) 

225,673 

519,556 

5,468,383 

273,265 

790,267 

6,615,046 

Total 

140.  Percentage  Analysis  of  a  Business.  Mr.  E.  C.  Barton  is 
the  proprietor  of  a  wholesale  store.  At  the  end  of  each  month  he 
analyzes  the  records  of  his  business.  The  following  analysis  was 
made  June  30,  1915.  Results  should  be  approximate  to  the  near- 
est liundredth  of  a  per  cent. 

1.  The  purchases  during  June,  1915,  were  -18146.90.  Some 
of  the  goods  purchased  were  defective,  and  were  returned.  The 
value  of  goods  returned  was  $123.60.  The  returned  goods  were 
what  per  cent  of  the  purchases  ? 


INCREASE  AND  DECREASE  175 

2.  Gross  sales  for  June,  1915,  were  111,216.29.  Goods  re- 
turned to  the  store  by  dissatisfied  customers,  $97.65.  The  re- 
turned sales  were  what  per  cent  of  the  gross  sales  ? 

3.  Gross  sales  for  June,  1914,  were  19862.15.  Returned 
sales,  f  101.80.  What  per  cent  of  the  sales  were  returned  in 
June,  1914  ? 

4.  What  was  the  increase  in  the  gross  sales,  and  what  was  the 
per  cent  of  increase  ? 

5.  Gross  Sales  —  Returned  Sales  =  Net  Sales. 

What  were  the  net  sales  for  June,  1914  ?  For  June,  1915  ? 
What  was  the  increase  in  net  sales,  and  the  per  cent  of  increase  ? 

6.  The  merchandise  on  hand  June  1, 1915,  was  worth  $  14,162.45 
at  selling  prices.  The  net  sales  for  the  month  were  found  in 
problem  5.  What  per  cent  of  the  stock  on  hand  at  the  beginning 
of  the  month  was  sold  during  the  month  ? 

7.  Net  Sales  —  Cost  of  Goods  Sold  =  Gross  Profit. 

The  gross  profit  for  June,  1914,  was  $1688.54.  The  gross  profit 
was  what  per  cent  of  the  net  sales  for  the  month  ?  (For  net  sales 
see  results  to  problem  5.) 

8.  The  gross  profit  for  June,  1915,  was  12001.36.  The  gross 
profit  was  what  per  cent  of  the  net  sales  for  that  month  ? 

9.  The  expenses  of  the  business  in  June,  1914,  were  $  1015.60. 
The  expenses  had  increased  in  June,  1915,  to  $1140.26.  What 
was  the  per  cent  of  increase  in  the  expenses  ? 

10.  Net  Sales  —  Gross  Profit  =  Cost  of  Goods  Sold. 
What  was  the  cost  of  goods  sold  in  June,  1914  ? 
What  was  the  cost  of  goods  sold  in  June,  1915  ? 

11.  Gross  Profit  —  Expenses  =  Net  Profit. 
What  was  the  net  profit  for  June,  1914  ? 
What  was  the  net  profit  for  June,  1915  ? 

12.  What  was  the  per  cent  of  increase  or  decrease  in  the  net 
profit  ? 

13.  Net  Profit  -h  Net  Sales  =  Per  Cent  of  Net  Profit  on  Sales. 
What  was  the  per  cent  of  net  profit  for  June,  1914  ? 

What  was  the  per  cent  of  net  profit  for  June,  1915  ? 


TRADING  ACTIVITIES.     PROFIT   AND   LOSS 

CHAPTER   XV 

BUYING   AND    SELLING   MERCHANDISE 

141.  The  Invoice.  When  a  merchant  sells  goods,  he  usually 
gives  the  customer  a  bill  or  invoice.  The  invoice  states  the  fol- 
lowing facts  : 

The  date  of  the  sale. 

The  name  and  address  of  the  seller. 

The  name  and  address  of  the  purchaser. 

The  terms  of  the  sale. 

A  detailed  list  of  the  articles  sold,  including  the  price  of  each 
item  and  the  total  of  the  invoice. 

If  prepaid  freight  is  to  be  charged  to  the  purchaser,  the  amount 
of  freight  is  added  to  the  invoice. 

If  the  invoice  has  been  paid,  a  statement  of  the  receipt  of  pay- 
ment is  made  by  the  seller. 

Study  the  following  invoice  and  state  as  many  as  possible  of  the 
facts  enumerated  above. 


TtltPHONE,  MAIN     1340 
PRIVATE  EXCHANfiE 

A.  B.  HUGHES 

DEALER  IN 

STAPLE  AND  FANCY  GROCERIES. 

211-213-215  Lake  Street, 

terms:                                                        ChicgoJlHooi. 

June  10,1915 

2?^  Cash  in  10  days ,                          SOLD  TO  Scobey  &  Company, 

Net  30  days.                                                              Fayette,  Iowa 

2  Cases    Tomato  Catsup        4doz. 

1.30 

5 

20 

6  Cases  Elgin  Canned  Corn   12  doz. 

1.10 

13 

20 

5  Cases    Echo  Peas        10  doz. 

1.25 

12 

50 

30 

90 

176 


BUYING  AND  SELLING  MERCHANDISE  177 

142.  What  the  Purchaser  Does.  After  the  purchaser  receives 
both  the  goods  and  the  invoice,  he  inspects  the  merchandise  to 
see  if  it  agrees  with  the  items  for  which  he  has  been  charged  on 
the  invoice.  If  stock  of  the  correct  kind  and  quantity  is  received, 
a  check  mark  is  entered  on  the  invoice  opposite  each  item  in  the 
column  at  the  left. 

The  invoice  is  next  checked  to  ascertain : 
a.    Whether  the  correct  prices  have  been  charged. 
h.    Whether  any  error  has  been  made  in  the  extension  of  the 
cost  of  each  item,  or  in  the  total  of  the  invoice. 

143.  Credit  Memorandum.  In  case  an  error  is  found,  notice  is 
sent  to  the  firm  from  which  the  goods  were  purchased.  When 
credit  is  to  be  given  by  the  seller  on  account  of  an  error  in  the 
invoice,  or  for  imperfect  goods,  or  for  any  other  cause,  the  pur- 
chaser will  usually  receive  a  credit  memorandum,  notifying  him 
of  the  amount  of  credit  entered  to  his  account. 


CREDIT  MEMORANDUM 

A.  B.  HUGHES 
CHICAGO. 

June  17,     19  15. 
TO    Williams  &  Co., 

Albany,  New  York 


Your  account  has  been  credited     $1,25 
On  account  of  overcharge  on  invoice  of  June  10,  1915 


Written  Work 

Check  the  invoice  on  page  176.  If  the  multiplications  are 
found  to  be  correct,  enter  a  check  mark  at  the  right  of  each 
item.  If  the  total  is  correct,  check 
it  also. 

When  an  invoice  has  been  checked 
and  found  to  be  correct,  the  exten- 
sions and  footings  are  checked  as 
shown  in  the  illustration. 


$16 

50/ 

23 

00/ 

4 

80/ 

$44 

30  • 

178  BUYING  AND  SELLING  MERCHANDISE 


Written  Work 

Find  the  totals  of  each  of  the  following  sales 
Apply  short  methods  when  possible. 

1. 

4  doz.  Men's  Irish  Linen  Handkerchiefs 

5  doz.  Men's  Hemstitched  Handkerchiefs 
14  doz.  Men's  White  Initial  Handkerchiefs 

9  doz.  Women's  Imported  Swiss  Embroidered 
Handkerchiefs 
22  doz.  Cliildren's  Linen  Handkerchiefs 

7  doz.  Women's  Swiss  Lawn  Handkerchiefs 
13  doz.  Children's  Mull  Handkerchiefs 

2. 

17  doz.    Men's  Leather  Gauntlets 

11  doz.    Men's  Buckskin  Gloves,  sizes  8  to  10 
16  pairs  Men's  Leather  Automobile  Mittens 
4|  doz.    Men's  Suede  Gloves,  sizes  7|  to  10 
3^  doz.    Men's  No.  J  264  Kid  Gloves 

6|  doz.    Imported  Kasan  Cape  Gloves 

3. 

16  Silk  Taffeta  Umbrellas 

28  8  Rib  Pure  Silk  Taffeta  Umbrellas 

32  Men's  Suit  Case  Umbrellas 

12  Extra  Size  Umbrellas 

4. 

3  doz.  pairs  Walton  Cotton  Blankets 
1  doz.  pairs  Cotton  Crib  Blankets 

8  doz.  pairs  Wool  Filled  Gray  Blankets 

7  doz.  pairs  Douglass  Wool  Finish  Plaids 

4  doz.  pairs  All  Wool  Plaids 

10  doz.  pairs  "  Canada  Camp  "  Blankets 

5. 

20  Assorted  Pattern  Smyrna  Rugs,  36  x  72 
80  Scotch  Jute  Rugs 
3  doz.  Cotton  Bathroom  Rugs,  27  x  54 


doz. 

14.431 

doz. 

5.38 

doz. 

3.23 

doz. 

2.16| 

doz. 

1.231 

doz. 

.67^ 

doz. 

.72i 

doz. 

$  7.68 

doz. 

9.49 

pair 

1.361 

doz. 

4.44 

doz. 

.  10.50 

doz. 

13.50 

each 

12.15 

each 

4.25 

each 

2.25 

each 

.87| 

pair 

$  .82 J 

pair 

.57^ 

pair 

3.85 

pair 

1.891 

pair 

6.00 

pair 

1.12J 

each 

12.25 

each 

.371 

each 

1.12J 

BUYING  AND  SELLING  MERCHANDISE  179 


6. 

3  doz.  Size  6     Children's  Fast  Black  Hose 
2  doz.  Size  6|   Children's  Fast  Black  Hose 

4  doz.  Size  7     Children's  Fast  Black  Hose 

5  doz.  Size  7^  Children's  Fast  Black  Hose 


6  doz.  Size  8  Children's  Fast  Black  Hose 
8  doz.  Size  8J  Children's  Fast  Black  Hose 

7  doz.  Size  9  Children's  Fast  Black  Hose 
6  doz.  Size  9|  Children's  Fast  Black  Hose 
5  doz.  Size  10  Children's  Fast  Black  Hose 


doz. 

il.171 

doz. 

1.21-1 

doz. 

1.24-1 

doz. 

1.27-1 

doz. 

1.311 

doz. 

1.421 

doz. 

1.491 

doz. 

1.61 

doz. 

1.66| 

7. 

20  No.  B  645  Silk  Woven  Waist  Patterns 

(each  pattern  31  yd.)  yd:     |.16§ 

25  No.  B  493  Dresden  Silk  Mull  Waist  Patterns 

(31  yd.  pieces)  yd.        .211 

18  bolts  Irish  Linette,  10,  II2,  12,  103,  ni^  ns^ 

121,  113^  103,  12,  10,  103,  101,  112^  12, 
113,  102,  103  yd.         J4I 

20  bolts  French  Gauze  Chiffon,  14,  133,  123,  141, 

14,  132,  13,  123,  13^  131^  142^  133^  142^ 
141,  133,  123,  14^  133^  132^  123  yd.        .371 

NoTK.    The  small  figures  mean  quarter  yards.     Thus  11-  means  11|  yards. 


Explanation  of  Grocery  Orders 

The  sign  f  if  placed  before  figures  means  "  number  " ;  if  placed  after  figures 
it  means  pounds. 

Articles  sold  in  cases  [cs.]  are  usually  priced  by  the  dozen.  The  total  num- 
ber of  dozens  in  the  cases  is  therefore  given  after  the  name  of  the  commodity, 
and  the  price  is  the  price  per  dozen. 

Some  articles  sold  in  barrels  and  cases  are  priced  by  the  pound ;  in  such 
instances  the  total  number  of  pounds  in  all  the  barrels  or  cases  appears 
immediately  before  the  price. 

Sugar  is  sold  by  the  hundred  pounds  (cwt.).  The  net  weight  of  each 
barrel  is  given.  Find  the  total  nunjber  of  pounds  ;  point  off  two  places  to  the 
left  to  find  the  number  of  hundred  pounds,  and  multiply  by  the  price  per 
hundred. 


180  BUYING  AND  SELLING  MERCHANDISE 


7  cases  Acme  Peas 

14  doz. 

Price 

.11.40 

3  boxes  Peona  Soap 

4.95 

7  bbh  Northern  Salt 

2.10 

15  bbL  Winter  Wheat  Flour  ^  sacks 

7.10 

12  bbl.  H.  &  E.  Granulated  Sugar 

329,  335,  347,  351,  344, 

347,  350,  331,  >342,  355, 

349,  333 

6.15  per  cwt, 

5  sacks  H.  &  E.  Granulated  Sugar 

500# 

6.10  per  cwt. 

9  cases  Acme  Peas 

18  doz. 

1.45 

17  cases  Acme  Corn 

34  doz. 

1.70 

6  boxes  Dried  Apples 

150# 

.08f 

2  bbl.  10  #  sacks  Northern  Salt 

1.95 

6  cases  Algonac  Tomatoes 

12  doz. 

1.37^ 

9. 

1  cs.  25  #  Macaroni 

$2.10 

5#  Cream  of  Tartar 

.40 

1  cs.  Acme  Peas 

2  doz. 

1.30 

5  cases  Hawthorne  Pears 

10  doz. 

2.95 

11  cases  Hawthorne  Peaches 

22  doz. 

2.50 

12  cans  Pimento 

.14 

15  cs.  H.L.  Shredded  Pineapple 

2.40 

10  cases  Tall  Salmon 

40  doz. 

2.10 

12  cases  F.  &  B.  Tomatoes 

24  doz. 

3.75 

85  sacks  Yellow  Corn  Meal 

850# 

.03 

8  cases  25  ^j^  Macaroni 

2.10 

5  cases  15  #  Spaghetti 

2.10 

7J  doz.  pkgs.  Seeded  Raisins 

1.40 

125  #  Rice 

.07 

25  quarts  Olive  Oil 

.75  gah 

18|  gal.  Sweet  Pickles 

1.06^ 

6J  gal.  Olives  |^ 

1.30 

25  cases  4  oz.  Grd.  Pepper 

125# 

.30 

6  cans  Paprika 

2.25  doz. 

14  cases  G.  M.  Soap 

2.85 

BUYING  AND  SELLING  MERCHANDISE  181 

12  cases  Soda  Crackers 

12  Cracker  cans 
1  tub  Peanut  Butter 
621  bbL  I  sacks  Spring  Wheat  Flour 
49f  bbl.  I  sacks  Winter  Wheat  Flour 

16  cases  #2  Algonac  Lima  Beans 

14  cases  #2  Algonac  String  Beans 

10. 

10  doz.  W/W  6  in.  Plates 
131  doz.  W/W  4  in.  Plates 

5  doz.  /S/  21  in.  Butter  Chips  Tk. 
8^  doz.  #13  Cups 

6  doz.  W/W  4  in.  Ice  Creams 

15  doz.  #64  /G/  Nappies 
8  doz.  A.C.  1  Tk.  30's  L/F  Bowls 
I  doz.  #211  Tea  Pots 

21  doz.  #0  /S/  Custard  Pots 

17  doz.  #1352  Tumblers 
12  doz.  #1296  Finger  Bowls 
If  doz.  #  3234  Oil  Bottles 

31  doz.  12-199  Salts 
3i  doz.  12-200  Peppers 
21  doz.  444  A  Pitchers 

J  doz.  Punch  Glasses 
121  doz.  3404  Dessert  Forks 
121  doz.  3405  Dessert  Knives 

16  doz.  3413  Tea  Spoons 
8  doz.  3406  Dessert  Spoons  2.25    doz. 

Rule  invoices  and  enter  the  following  sales,  assuming  that  you 
a^e  the  selling  merchant. 

11.    To  W.  K.  Sears, 

Elgin,  Illinois. 

Sept.  10. 
45  No.  R  721  Body  Brussels  Rugs    6x9    ft.  each  f  13.25 

32  No.  R  731  Body  Brussels  Rugs    8  x  10  ft.  each    19.75 


m* 

Prick 

$  .09 
.50 

48i# 

.121 
5.80 

6.25 

32  doz. 

1.40 

28  doz. 

1.371 

f  .82    doz. 

.62J  doz. 
.22    doz. 

.87.1  doz. 

.44    doz. 

1.121  doz. 
1.28^  doz. 

1.25    doz. 

.98    doz. 

.45    doz. 

1.331  doz. 

2.25    doz. 

1.50    doz. 

1.50    doz. 

5.00    doz. 

.75    each 

2.35    doz. 

2.30    doz. 

1.371  doz. 

182  BUYING  AND  SELLING   MERCHANDISE 

Prick 

36  No.  R  741  Body  Brussels  Rugs    9  x  12  ft.  each  $22. 87 J 
25  No.  R  751  Body  Brussels  Rugs  11  x  13  ft.  each    30.80" 


12.    To  C.  B.  Perkins, 

Amherst,  Minn. 

Sept.  12. 

20           H  20    Family  Coffee  Mills 

each 

$1.35 

16  sets  H  33    Sad  Irons 

set 

.73 

12  doz.  H  545  Flour  Sifters 

doz. 

1.83J 

25  doz.  H  463  Carpet  Beaters 

doz. 

.89 

8  doz.  H  6646  Galvanized  Clothes  Lines, 

20  gauge  wire. 

doz. 

.92| 

10  doz.  H  6546  Galvanized  Clothes  Lines, 

18  gauge  wire, 

doz. 

1.52| 

13.    To  Owen  &  Hendersen, 

Cedar  Rapids,  Iowa. 
Sept.  13. 
35  F  384  Plush  Library  Chairs  each  $14.75 

28  F  376  Reed  Rockers  each       3.10 

18  F  394  Bedroom  Rockers  each      4.85 
26  F  465  Roman  Chairs                          each       7.88 

19  F  414  Morris  Chairs  each     18.95 


CHAPTER   XVI 
COMMERCIAL  DISCOUNTS 

Cash  Discount 

144.  Purpose  of  Cash  Discount.  In  order  to  encourage  prompt 
settlement  of  accounts,  merchants  frequently  offer  to  deduct  a  cer- 
tain per  cent  of  the  bill  if  it  is  paid  within  a  fixed  number  of  days. 
This  deduction  for  prompt  payment  is  called  cash  discount. 

145.  Terms.  The  terms  state  the  discounts  offered  and  the 
time  when  the  bill  is  due.  The  terms  are  often  expressed  by  an 
arrangement  similar  to  the  following  : 

2/10;  1/30;  N/60. 

The  figures  at  the  left  of  the  line  indicate  the  rate  of  discount 
offered;  the  figures  at  the  right  indicate  the  number  of  days 
within  which  payment  must  be  made  in  order  to  obtain  the  dis- 
count.    Thus,  the  terms  stated  above  mean  : 

2  %  discount  from  the  face  of  the  bill,  if  paid  in  10  days ; 

1  %  discount  from  the  face  of  the  bill,  if  paid  in  30  days ; 

Net  Amount  (no  discount  is  allowed,  and  bill  is  due)  in  60  days. 

146.  Definitions.  The  amount  of  the  purchase  before  subtract- 
ing the  discounts  is  called  the  list  price. 

The  amount  of  the  purchase  after  subtracting  the  discounts  is 
called  the  net  price. 

The  Rate  of  Discount  is  stated  as  a  per  cent  of  the  list  price. 

147.  Cash  Discount  Illustrated.  The  terms  of  the  invoice  on 
page  176  were  2/10 ;  N/30. 

In  order  to  obtain  the  discount,  Scobey  &  Co.'s  payment  must 
be  made  on  or  before  June  20,  1915. 

The  bill  is  due  and  payment  is  expected  in  full  on  July  10,  1915. 

No  discount  is  allowed  if  payment  is  made  between  June  20  and 
July  10,  1915. 

183 


184  COMMERCIAL  DISCOUNTS 

148.  Computing  the  Discount  and  the  Net  Price. 

First  Method  : 

195.25  List  price 

.02  Rate  of  discount 

$1.9050  Discount 

$95.25     List  price 
1.91     Discount 
$93.34     Net  price 
State  a  rule  for  finding  discount  and  net  price  by  this  method. 
(Note  that  five  mills  or  more  in  the  discount  are  considered  a 
cent.     Thus,  $1,905  is  considered  $1.91.) 

Second  Method : 

100  %  List  price 

2<^  Rate  of  discount 

98  %  Per  cent  of  bill  to  be  paid 

$95.25       List  price 

.98 
$93,345     Net  price 
or  $93.34 
State  a  rule  for  computing  the  net  price  by  this  method. 

149.  The  Advantages  of  Cash  Discount.  Cash  Discounts  may 
benefit  both  the  purchaser  and  the  seller.  Merchants  offer  cash 
discounts  because  they  encourage  prompt  payments,  and  thus 
decrease : 

a.    the  loss  from  bad  debts ; 

5.    the  cost  of  collecting  accounts ; 

c.    the  amount  of  capital  tied  up  in  outstanding  accounts. 

It  is  usually  good  business  for  the  purchaser  to  "take  his  dis- 
count" (pay  the  bill  before  it  is  due),  even  though  the  rate  of 
discount  may  be  small.     An  illustration  will  show  this  fact. 

Suppose  the  terms  of  the  sale  are.  Cash  less  1  % ;  net  30  days. 
If  the  purchaser  pays  cash,  he  receives  1  %  for  the  use  of  his  money 
for  one  month.  1%  a  month  is  12%  a  year;  a  high  rate  of 
interest. 


CASH  DISCOUNT  .      185 

The  rates  of  cash  discount  are  usually  small,  varying  from  1  % 
to  5%. 

Small  discounts  are  offered  if  the  bill  is  due  in  a  short  time. 

For  example,  1/10  ;  N/30. 

Larger  discounts  are  offered  if  the  bill  is  due  after  a  greater 
length  of  time. 

For  example,  5/30  ;  N/4  months. 

As  a  further  means  of  insuring  payment  of  invoices,  merchants 
frequently  charge  interest  on  bills  which  are  not  paid  when  due. 

Written  Work 

Find  the  list  price,  the  discount,  and  the  net  price  of  each  of 
the  following  purchases,  and  answer  the  following  questions  about 
each  invoice. 

a.  What  is  the  last  day  on  which  payment  can  be  made  and  the 
discount  secured  ? 

h.    When  is  the  invoice  due  ? 

1.  Invoice  dated  April  4.     Terms  2/10 ;  N/80. 

7  cases  Acme  Peas $1.40 

3  cases  Osea  Soap 4.95 

7  bbl.  Northern  Salt 2.10 

15  bbl.  i  sacks  A.  D.  Flour 7.10 

2.  Invoice  dated  October  26.     Terms  1/15;  N/80. 

12  bbl.  H.  E.  Granulated  Sugar,  329,  335,  347,  351,  344, 

347,  350,  331,  342,  355,  349,  333  # $6.15 

5  sacks  H.  E.  Granulated  Sugar,  500  # 6.10 

3.  Invoice  dated  January  5.     Terms  2/10  ;  1/20;  N/80. 

16  bolts  White  Dress  Linen,  10,  12,  11^,  122,  iqs,  ip^ 

103,12,101,112,12,111,102,113,121,102     ...  yd.  ^.44^ 
12  bolts  Persian  Lawn,  248,  25i,  232,  95,  242,  248,  252, 

241,238,248,252,25 yd.  .171 

48  bolts  French  Nainsook,  12-yard  pieces      ....  yd.  .18^ 

36  bolts  Mercerized  Lingerie  Batiste,  24-yard  pieces  .  yd.  .21 

24  bolts  Imported  Linen  Lawn,  10-yard  pieces  ...  yd.  .43| 

Note.     There  will  be  two  possible  net  prices  for  this  invoice. 


186 


COMMERCIAL   DISCOUNTS 


4.    Complete  the  following  table. 

Combine  the  dollars  in  the  column  at  the  left,  with  the  cents  in 
the  row  near  the  top,  to  form  the  list  price.  Deduct  the  discount 
shown  above  the  cents,  and  enter  the  net  price  in  the  table.  The 
two  results  entered  in  the  table  show  the  method.     Thus, 


$26.10  the  list  price 

.02  the  discount 

$     .52  the  discount  at  2  % 

126.10 

^ 

$25.58  Xet  price 


$641.67 
.025 
$   16.04  the  discount  at  2|  % 

$641.67 
16.04 
$  625.63  Net  price 


Less  2  % 

Less  5  % 

Lkss  3  % 

Less  2^  % 

10 

45 

75 

67 

$26 

00 

$25 

58 

14 

00 

73 

00 

19 

00 

261 

00 

112 

00 

317 

00 

216 

00 

641 

00 

$625 

63 

In  this  exercise  and  in  many  which  follow,  it  is  not  expected  that  each 
student  will  complete  the  entire  table.  The  work  may  profitably  be  distributed 
among  the  students. 

Trade  Discount 

150.  Purpose  of  Trade  Discount.  In  some  lines  of  business 
merchants  sell  both  at  wholesale  and  retail.  They  advertise  their 
goods  at  a  certain  price,  but  when  they  sell  to  dealers,  they  fre- 
quently deduct  a  part  of  this  price.  The  amount  deducted  is 
called  a  Trade  Discount. 

Trade  discounts  are  most  common  in  businesses  which  issue 
catalogues.  When  the  catalogue  is  sent  to  a  dealer,  a  discount 
sheet  is  inclosed. 


TRADE  DISCOUNT 


187 


Specimen  Discount  Sheet 

Discount  Sheet 

The  following  discounts  are  offered  on  articles  listed  in  catalogue  No.  A  23. 

Pages    1  to  15 20  % 

Pages  16  to  3.9 28  % 

Pages  39  to  67 40  % 

Pages  68  to  90 Net 

Pages  91  to  136 14f  % 

Do  not  show  this  discount  sheet  to  your  customers. 


Note.     "Pages  68  to  90  Net"  means,  no  trade  discount  is  offered  for  goods 
listed  on  these  pages. 


Not  Responaible  for  aoods  Lost  or  Damaged  in  Transit.  Claims  for  Allowance  must  be  made  upon  Receipt  of 
Ooods.  Address  all  Communications  to  Abworombie  A  Co.,  Chicago 

ABERCROMBIE  &  COMPANY 

PUBLISHERS  &  BOOKSELLERS 
245  WABASH  AVENUE 

CHICAGO.  March  3,  19  15 

SOLD  TO  W.  M.  Rickert  Co., 

Home, 

jQ^j^                                            YOUR  ORDER  NO.       121 
TERMS.       ,2/10;  N/30 
CONVEYANCE,    U.  S.  Ex. 

IN    REFERRING  TO  THIS   ORDER    MENTION    NO.  4336                  ENTERED       W.    B.3/3/l5. 

12 

21 

Copies  H.&  J.  SecondYear  English  .85 
»•      Beeman's  Algebra                     .90 

Less  1836 

10 
18 

20 
90 

23 

86 

29 
5 

10 
24 

188 


COMMERCIAL  DISCOUNTS 


Class  Discussion 

1.  Why  do  merchants  offer  trade  discounts  ? 

2.  What  is  the  catalogue  price  of  the  H.   &  J.  Second  Year 
English  per  copy  ? 

3.  How  much  does  each  copy  of  the  English  book  actually  cost 
the  retail  dealer  ? 

4.  If  Mr.   Rickert  sells  this  book  for  the  catalogue  price,  85 
cents,  how  much  profit  does  he  make  on  each  book  ? 

5.  Trade    discounts   are   usually   larger  than   cash   discounts. 
Why  do  you  think  this  is  the  case  ? 


151.    Computing  Trade  Discounts.     Trade   discounts  are   com- 
puted in  the  same  manner  as  cash  discounts. 

Example.     What  will  goods  cost  a  dealer  if  they  are  sold  to 
him  for  $46,  less  a  trade  discount  of  25%  ? 


Solution.     $46.00  List  price 

.25  Rate  of  discount 
$11.50  Trade  discount 


$46.00  List  price 

11.50  Trade  discount 
$  34.50  Price  to  dealer 


Written  Work 


Complete  the  following  table, 
deducting  the  Trade  Discount. 


Enter  the  price  to  dealer  after 


Catalog  iTB  Price 

Trade  Discount 

$27 

85 

$126 

39 

$96 

45 

14?% 

18% 

20% 

22% 

25% 

15%      • 

17% 

28% 

16f% 

10% 

TRADE  DISCOUNT 


189 


152.  Series  of  Two  Discounts.  Invoices  are  often  subject  to  a 
cash  discount  in  addition  to  the  trade  discount.  Two  or  more  dis- 
counts are  called  a  "  Discount  Series." 

Example.  What  is  the  smallest  amount  of  money  that  will  pay 
a  bill  of  tf  236,  subject  to  a  trade  discount  of  20%  and  a  cash  dis- 
count of  2  %  ? 


Solution. 
if  236.00  List  price 

.20  Rate  of  trade  discount 
$  47.20  Trade  discount 
$236.00  List  price 

47.20  Trade  discount 
$188.80  Price  to  the  trade 


$188.80  Trade  price 

.02  Rate  of  cash  discount 
$3.7760  Cash  discount 
$  188.80  Trade  price 

3.78  Cash  discount 
$  185.02  Net  price 


The  cash  discount  is  computed  on  the  trade  price,  not  on  the 
list  price.  Therefore,  20  %  trade  discount  and  2  %  cash  discount 
are  not  the  same  as  a  single  discount  of  22  % . 

Written  Work 

Complete  the  following  table.  From  each  list  price  deduct  the 
trade  discount  indicated  above  the  list  price;  and  from  the  trade 
price  thus  found,  deduct  the  cash  discount  shown  at  the  left. 


Cash  Discount 

Facts  to  bk  Found 

Trade  Discount, 

2S%- 

Trade  Discount, 
25% 

Trade  Discount, 

List  Price 

$36 

45 

$68  40 

$239 

64 

Trade  Discount 

2% 

Trade  Price 
Cash  Discount 
Net  Price 

List  Price 

205 

08 

333 

95 

47 

30 

Trade  Discount 

3% 

Trade  Price 

Cash  Discount 
Net  Price 

List  Price 
Trade  Discount 

35 

00 

713 

20 

609 

49 

5% 

Trade  Price 
Cash  Discount 
Net  Price 

190  COMMERCIAL  DISCOUNTS       • 

Quantity  Discounts 

153.  Purpose  of  Quantity  Discounts.  In  some  lines  of  business, 
particularly  in  manufacturing,  it  is  customary  to  give  a  larger  rate 
of  discount  on  a  large  order  than  on  a  small  one. 

A  mail  order  firm  advertises  : 

1  %  discount  on  an  invoice  of  |10  ;   2  %  on  120 ;  5  %  on  $B5. 

What  is  the  purpose  of  such  quantity  discounts  ? 

A  printer  advertised  the  following  rates: 

f  10  per  thousand  for  the  first  thousand  copies.  On  an  order  of 
more  than  1000  copies,  a  discount  of  15  %.  This  discount  is 
offered  because  the  work  of  typesetting,  making  up  the  forms, 
and  making  ready  the  press  must  all  be  done,  although  only  one 
copy  is  to  be  printed.  The  cost  of  printing  2000  copies,  there- 
fore, is  not  twice  as  much  as  for  1000  copies. 

Written  Work 

1.  The  following  prices  were  quoted  by  a  manufacturer  of 
lockers:  No.  6094.     Each  $6.30. 

Discounts : 

Orders  of  from    50  to  100  —  Less  8  %. 
Orders  of  from  101  to  300  —  Less  10  %. 
Orders  of  from  301  to  500  —  Less  12^  %, 

Find  the  total  cost  and  the  cost  per  locker  of  an  order  of  75 
lockers;  140;  475. 

2.  A  paper  manufacturer  quoted  the  following  prices: 
No.  020  note  paper,  cut  to  size  8  by  10,  $.55  per  ream. 

An  extra  charge  of  3  cents  per  ream  will  be  made  for  wrapping 
in  packages  of  500  sheets.     (500  sheets  considered  1  ream.) 

On  orders  of  100  reams  or  more  a  discount  of  4  %  will  'be 
allowed. 

Terms,  1/10  ;  N/30. 

Find  the  cost  and  state  what  discounts  were  allowed : 

a.  An  order  of  50  reams,  unwrapped,  payment  made  20  days 
from  date  of  sale. 


TRADE  DISCOUNT  191 

h.  An  order  of  150  reams,  unwrapped,  payment  made  15  days 
from  date  of  sale. 

c.  An  order  of  150  reams,  wrapped,  payment  made  18  days  from 
date  of  sale. 

d.  An  order  of  240  reams,  wrapped,  payment  made  7  days  from 
date  of  sale. 

e.  An  order  of  60  reams,  wrapped,  payment  made  8  days  from 
date  of  sale. 

Fluctuation  Discount 

154.  Purpose  of  Fluctuation  Discounts. 

Another  important  discount  is  that  offered  to  change  the  cata- 
logue price  of  an  article  to  meet  the  changes,  or  fluctuations,  in 
the  market  price.  Fluctuation  discounts  are  used  by  establish- 
ments which  sell  goods  made  from  raw  material  the  price  of  which 
frequently  changes. 

For  example,  suppose  an  article  made  from  steel  (the  market  price  of  which 
varies  at  frequent  intervals)  is  quoted  in  the  catalogue  at  $8. 

When  the  market  price  of  steel  drops  and  the  article  can  be  sold  for  $  7,  a 
discount  of  12 A  %  can  be  offered. 

If  raw  steel  should  drop  in  price  so  that  the  article  could  be  sold  for  ^6,  a 
discount  of  25  %  could  be  offered. 

The  fluctuation  discount  sheet  is  a  means  of  economy  to  the 
manufacturer,  because  he  can  issue  new  discount  sheets  much  more 
cheaply  than  complete  catalogues. 

155.  Computing  Fluctuation  Discounts. 

Example.  What  discount  will  change  a  catalogue  price  of  13 
to  a  market  price  of  $  2.50  ? 

Solution.     $3.00     Catalogue  price 

2.50     Price  at  which  article  is  to  be  sold 
$    .50     Amount  to  be  deducted  by  discount 
f  .50  -4- 13.00  =  16|  %,  rate  of  discount  to  be  offered 

State  a  rule  for  finding  the  rate  of  discount  by  this  method. 

When  the  quotient  obtained  by  the  division  involves  a  frac- 
tional  per  cent,  the  next  lower  whole  number  is  sometimes  taken 
as  the  per  cent.  Thus,  a  quotient  of  lb\  %  may  be  regarded  as 
15  %  ;  a  discount  of  18.27  %  may  be  regarded  as  18  %. 


192 


COMMERCIAL  DISCOUNTS 


Example.  An  article  is  listed  at  124.50.  The  market  condi- 
tions  are  such  that  it  should  sell  for  about  121.30.  What  rate  of 
discount  should  be  offered  ? 

Solution.    $24.50    List  price 

2L30    Market  price 
$   3.20     Amount  to  be  deducted  by  discount 
^3.20  H- $24.50  =  13.06%. 
13  %  would  therefore  be  offered. 
This  discount  would  make  the  net  price  $     .     ?    ' 

Written  Work 

Complete  the  following  table,  showing  what  rate  of  discount 
would  be  offered  to  reduce  the  list  prices  at  the  left  to  the  market 
prices  shown  at  the  top  of  the  table. 

Express  results  to  the  nearest  per  cent. 


Market  Prices 

List  Pkices 

$8 

50 

$7 

75 

$8 

00 

$7 

60 

$6 

00 

$10 

12 

11 

9 

10 

00 
00 
50 
80 
50 

Discount  Series 

156.   Trade  and  Fluctuation  Discounts  Combined. 

Some  business  concerns  offer  an  unchanging  trade  discount  and 
a  changing  fluctuation  discount.  This  slightly  increases  the 
task  of  determining  what  fluctuation  discount  to  offer. 

Example.  An  article  is  listed  at  $  12  less  a  trade  discount  of 
25%.  The  market  value  drops  so  that  the  real  net  price  should 
be  f  6.     What  additional  discount  must  be  offered  ? 

Solution.  $12  x  .25  =  $3,  Trade  discount. 

$  12  -  $3  =  $  9,  Price  less  trade  discount. 
,^9  -  16  =  $3,  amount  to  be  deducted  by  2d  discount. 
$3  H-  $9  =  33^%,  rate  of  fluctuation  discount. 


tra.de  discount 


193 


Written  Work 

Complete  the  following  table. 

The  columns  at  the  left  show  the  list  price  and  the  trade  dis- 
count offered.  Find  what  fluctuation  discount  must  be  offered 
to  reduce  the  price  to  market  values. 

Approximate  results,  correct  to  the  nearest  hundredth  of  a  per 
cent. 


Trade 
Discount 

Market  Values 

124 

00 

$23 

50 

$22 

00 

$20 

00 

^28 
33 
30 
40 

00 
00 
50 
00 

10% 

15 

12 

28 

Written  Review 

1.  An  implement  dealer  purchased  the  following  invoice : 
Dated  April  17. 

4  No.  364  Plows,  $38.75,  less  20  %. 

7  Self  Dump  Hay  Rakes,  $  20.50,  less  18  %. 

7  No.  264  Hay  Stackers,  $41.50,  less  15  %. 
Terms,  2  %  for  Cash  in  20  days.     Net  90  days. 
On  May  2,  he  paid  the  bill  with  a  check  for  $ . 

2.  Which  of  the  following  prices  is  better  for  the  purchaser  : 
145,  less  25  %,  18  %,  and  2  %  ; 

160,  less  28  %,  25  %,  and  1  %  ? 

3.  A  merchant's  discounts  were  25  %  and  15  %.  A  clerk  sold 
an  invoice  of  172  and  gave  a  single  discount  of  40%.  How 
much  did  his  error  cost  his  employer  ? 

4.  A  merchant  lists  a  desk  at  $45  less  20  %.  A  competitor 
sells  a  similar  desk  for  $48  less  33^  %.  In  order  to  exactly  meet 
his  competitor's  price,  the  first  merchant  decides  to  give  an  addi- 
tional discount  of  —  %. 


194 


COMMERCIAL  DISCOUNTS 


5.  Hewett  paid  an  invoice  in  time  to  secure  a  discount  of  3  %. 
If  the  check  sent  was  for  f  208.55,  what  was  the  list  price  of  the 
invoice  ? 

6.  Graff  Brothers  sent  a  check  to  a  wholesale  house  to  pay  an 
invoice.  The  check  was  for  f  801.90.  What  was  the  list  price 
of  the  invoice  if  the  discounts  taken  were  10  %  and  1  %  ? 

157.  A  Short  Method  of  Finding  a  Single  Discount  Equivalent  to 
a  Discount  Series.  A  single  discount  equivalent  to  two  discounts 
may  be  found  as  follows: 

From  the  sum  of  the  two  discounts  subtract  their  product. 
The  rule  may  be  easier  to  remember  if  stated  thus: 
Add  the  two  discounts;  multiply  the  two  discounts;  subtract  the 
second  result  from  the  first. 

Example.  What  single  discount  is  equivalent  to  a  trade  dis- 
count of  20  %  and  a  cash  discount  of  2  %  ? 


Solution. 


.20  +  .02  =  .22 
.20  X  .02  =  m^ 
Single  discount  =  .216  or  21.6% 


The  buyers  in  some  large  business  houses  prepare  an  elaborate 
table  similar  to  the  one  which  follows.  When  manufacturers 
quote  prices  subject  to  a  discount  series,  the  buyers  can  tell  by  a 
glance  at  the  table  what  single  discount  the  series  equals. 


Written  Work 


Complete  the  following  table,  using  the  method  just  explained 
to  find  single  discounts  equivalent  to  the  discount  series. 


Trade 
Discount 


18% 

15 

20 

25 

33i 


Cash  Discount, 

8% 


Cash  Discount, 

6% 


Cash  Discount, 

5% 


Cash  Discount, 

1% 


Cash  Discount, 
10% 


TRADE  DISCOUNT  195 

With  the  aid  of  the  table,  find  the  net  price  of  the  following: 
a.    An  invoice  of  §215,  less  18  %  and  5  %. 
h.    An  invoice  of  8464.20  less  18  %  and  10  %. 

c.  An  invoice  of  1 12.40  less  20  %  and  6  %. 

d.  An  invoice  of  -f  23.87  less  83^  %  and  3  %. 

158.   Series  of  Three  Discounts. 

It  sometimes  happens  that  a  bill  is  subject  to  several  discounts. 
Explain  how  this  might  be  the  case. 

To  find  the  net  price  of  a  bill  subject  to  three  discounts,  find 
the  discount  equivalent  to  two  of  the  discounts  stated,  then  find 
the  discount  equivalent  to  this  result  and  the  third  discount. 

Example.  What  discount  is  equivalent  to  three  discounts  25  %, 
20%,  10%? 

Solution.  First  find  the  discount  equivalent  to  discounts  of  25  %  and 
20%;  the  result  is  40%. 

Find  the  discount  equivalent  to  discounts  of  40  %  and  10  %  ;  the  result  is  46  %. 
Therefore  a  discount  of  46  %  is  equivalent  to  discounts  of  25  %,  20  %,  10  %. 

Written  Work 
Find  the  net  cost  of  the  following  bills : 

1.  {5> 45  less  discounts  of  20%,  15%,  and  10  %. 

2.  128  less  discounts  of  25  %,  10  %,  and  5  %. 

3.  $  70  less  discounts  of  30  %,  20  %,  and  2  %. 

Find  a  single  discount  equivalent  to  each  of  the  following 
series: 

4.  20  %,  121  %,  and  8  %.  5.    15  %,  10  %,  and  4  %. 
6.    28%,  14%,  and  2%.  7.    25  %,  20  %,  and  10  %. 

8.    40%,  20%,  and  10%.  9.    33^  %,  20  %,  and  121  %. 

10.    371  %,  10  %,  and  20  %. 


CHAPTER   XVIT 
RECORDING  PURCHASES  AND  SALES 

159.  The  Purchases  Book.  Merchants  usually  keep  a  record  of 
purchases  and  sales.  There  are  several  different  kinds  of  books 
used  for  this  purpose.  The  following  illustration  shows  a  com- 
mon form  of  the  Purchases  Book. 


PURCHASES  BOOK 

Date  of 
Invoice 

From  Whom  Purchased 

Amount 

Termt 

Discount 

terra 
Expire. 

Csh 
Diicount 

Due 
Date 

When  &  How  Peid 

/f/S 

» 

M^U^t,^^^^^^ 

S.3 

8/(, 

^/<5;^A 

^e^ 

/^ 

iAH 

a/t^ 

i^ 

m^ 

/A 

2/^-^ 

The  entries  in  the  purchases  book  are  made  from  the  invoice 
received  at  the  time  of  the  purchase.  The  model  shows  proper 
record  of  the  purchase  made  from  Abercrombie  &  Co.,  as  shown 
by  the  invoice  on  page  187. 

Notice  that  $23.86  is  the  amount  of  the  invoice  after  deducting 
the  trade  discount  of  18%.  The  cash  discount  is  not  deducted 
until  the  bill  is  paid. 

The  terms  are  taken  from  the  invoice. 

The  discount  term  expires  March  13.  It  is  important  to 
have  this  date  recorded  in  the  purchases  book,  as  it  is  the  last 
date  on  which  payment  may  be  made  and  the  discount  secured. 

April  2  is  the  day  when  the  bill  is  due  and  payment  is  ex- 
pected. No  discount  is  allowed  when  payment  is  made  between 
March  18  and  April  2. 

160.  How  to  find  the  Date  when  an  Invoice  is  Due.  If  the  terms 
are  stated  in  days,  count  the  actual  number  of  days.  Thus,  30 
days  from  March  3  is  April  2. 

196 


RECORDING  PURCHASES  AND  SALES 


197 


If  the  terms  are  stated  in  months,  calendar  months  are  counted. 
Thus,  if  the  terms  had  been  2/10 ;  N/1  month,  the  invoice  would 
have  been  due  on  April  3. 

No  entry  is  made  in  the  "  When  and  How  Paid  "  column  until 
the  invoice  is  paid. 

It  is  not  necessary  to  enter  the  items  in  the  purchases  book, 
because  the  invoice  can  be  kept  on  file  to  supply  this  information. 

161.  The  Sales  Book.  The  following  illustration  shows  a  page 
from  a  commonly  used  form  of  sales  book. 

The  entries  were  made  from  the  invoice  on  page  187. 


^%;;Z>fc<5^^.    /^/^ 

^^9&.^^^.                  ^..^.  <=£^.^  1 

cA^..^<^.^/o.      ^/3o 

/2*g^^*.^^P^^.g^..^>*^^^^^(^^:^^.^     ^S 

/O 

2^ 

^f           /.           SS^^-rrz^,^,^  C^l^^J-i-.^                          .^^ 

/3 

^ 

^                                               '^^ 

JP.C7 

/O 

^,^.UU  /g% 

^ 

d^ 

^.7^ 

S(^ 

162.  Loose-leaf  Sales  Book.  Many  merchants  record  their  sales 
in  a  loose-leaf  sales  book.  At  the  time  the  invoice  is  made,  a 
carbon  copy  is  also  made.  This  requires  very  little  extra  labor, 
and  the  carbon  copies,  called  "Charge  Sheets,"  having  holes 
punched  at  the  side,  can  be  bound  together  in  a  binder. 

The  loose-leaf  sales  book  has  several  advantages.  Both  the  in- 
voice and  the  charge  sheet,  which  forms  the  sales  book,  can  be 
made  on  the  typewriter  at  the  same  time ;  and  fraud  is  prevented 
because  the  invoices  are  numbered,  and  a  clerk  cannot  sell  goods 
and  make  an  invoice  without  also  making  a  charge  slip.  He  cannot 
keep  the  money  and  destroy  the  charge  slip  because  one  of  the  num- 
bered sheets  would  be  missing,  and  the  fraud  would  be  apparent. 

The  following  illustration  shows  the  charge  sheet  made  as  a 
carbon  copy  of  the  invoice  shown  on  page  187. 


198 


RECORDING   PURCHASES  AND  SALES 


terms: 

2^  C&8h  in  10  days, 
Net  30  days. 


CHARGE 


June  10,  1915 


Scobey &  Company, 
Fayette,  Iowa 


2  Cases  Tomato  Catoup   4  doz. 
6  Cases  Elgin  Canned  Corn  12  doz. 
5  Cases  Echo  Peas   10  doz. 


1.30 
1.10 
1.25 


30 


90 


Written  Work 

Rule  a  Purchases   Book  and  record  the  following  purchases, 
making  proper  extensions. 

1.    From    Eaton    &    Dunham,   213    Main    Street,   Indianapolis, 
Indiana. 

Date,  June  5,  1915. 
Terms,  1/15 ;  N/60. 
6  doz.  Silk  Four-in-hand  Ties 
3  doz.  White  Lawn  Ties 
38  doz.  Assorted  Style  Amoryth  Linen  Collars 
18  doz.  Policeman's  Suspenders 
9  doz.  Khaki  Overalls 

6  doz.  Boys'  Flannelette  Waists  (ages  4  to  13  yr.)  doz. 
10  doz.  Men's   Flannel   Work    Shirts    (sizes    14 

to  18) 
2\  doz.  Men's  Negligee  Shirts  doz. 


each 

t     .371 

gross 

2.94 

doz. 

1.92 

doz. 

4.374 

doz. 

8.97 

doz. 

2.16| 

doz. 

8.761 

16.40 


doz. 

14.29 

doz. 

4.78 

doz. 

6.93 

each 

2.17 

each 

2.98 

doz. 

6.93^ 

doz. 

4.69. 

doz. 

4.25 

RECORDING   PURCHASES  AND  SALES  199 

2.  From  J.  B.  Clark,  Aurora,  Illinois. 

Date,  June  8,  1915. 
Terms  2/20  ;"  N/3  months. 
7  doz.  Assorted  Sizes  Men's  Silk  Half  Hose 
19^  doz.  Mercerized  Lisle  Hose 
3  doz.  Men's  Black  Overgaiters 
18  Women's  Taffeta  Silk  Waists  (sizes  34 

to  42) 
24  Navy  Blue  Silk  Chiffon  Waists 

5  doz.  Embroidered  Lace  Coat  Sets 
2  doz.  Amoskeag  Gingham  Aprons 
2J  doz.  Lace  Jabots 

3.  From  Bishop  &  McGee,  Independence,  Iowa. 

Date,  June  10,  1915. 
Terms,  1/5;  N/20. 
10  doz.  Defiance  Food  Choppers  each       1 2. 85 

9  doz.  Climax  Food  Choppers  each  .72 

14  doz.  No.  7  size  Skillets  each  .22i 

30  sets  Enamel-lined  Iron  Kettles,  each  set  con- 
taining 

3  2  quarts  at  .21 

4  4  quarts  at  .29| 
6  6  quarts  at  .34| 
4  8  quarts  at  .39| 
2  10  quarts  at  .46| 

2f  doz.  H  921  Waffle  Irons 
61  doz.  H  922  Waffle  Irons 


doz. 

$7.84| 

each 

.93 

each 

.55 

each 

,65% 

25  H464  Soapstone  Griddles  (round) 

12  doz.  H465  Soapstone  Griddles  (oval) 

4.    From  A.  D.  McHaughtoir,  Fairchild,  Missouri. 
Date,  July  14,  1915. 
Terms,  3/30 ;  N/90. 
5  doz.  H  731  Wire  Waste  Baskets  doz.       I   .89 

15  doz.  H  732  Wire  Letter  Baskets  doz.         1.23 

28  H  881  Spring  Seats  each  .88 


200  RECORDING  PURCHASES  AND  SALES 

15  sets  H  393  Cobblers' Outfits  set      I      .96 

19  doz.  H  242  Curry  Combs  doz.  .6T 
14  F  272  Upholstered  Rockers  each  8.75 
25          F  279  Oak  Rockers                                         each       12.65 

20  F  212  Turkish  Rockers  each       12.75 

Rule  a  Sales   Book,  and   record   the  following   sales,  making 
proper  extension. 

5.  To  J.  D.  Preston,  Monmouth,  Illinois. 

July  7,  1915. 

Terms,  1/10 ;  N/40. 

47  No.  L  601  Royal  Worsted  Wilton  Rugs  8  x  10  ft.  each  $  29.25 

52  No.  L  602  Royal  Worsted  Wilton  Rugs  6x7  ft.  each  19.75 

38  No.  L  603  Royal  Worsted  Wilton  Rugs  9x12  ft.  each  32.35 

65  No.  L  661  Worsted  French  Wiltons      9  x  12  ft.  each  44.60 

50  No.  L  662  Plain  Color  Wiltons               8  x  10  ft.  each  31.75 

6.  To  R.  J.  Noble,  Dubuque,  Iowa. 

July  8,  1915. 
Terms,  1/15 ;  N/60. 

25  doz.  Half-bleached  Cotton  Towels 

16  doz.  Linen  Monogram  Towels 
20  doz.  Bleached  Turkish  Bath  Towels 

14  doz.  No.  T  291  Cotton  Face  Cloths 

7.  To  Oscar  Hamilton,  Reynolds,  North  Dakota. 

July  9,  1915. 

Terms,  2/5  ;  N/2  months. 

15  doz.  Palmetto  Fiber  Scrub  Brushes 
22  doz.  H  221  Kitchen  Spoons,  10  inch 
19  doz.  H  241  Kitchen  Spoons,  12  inch 

26  doz.  H  251  Kitchen  Spoons,  1*4  inch 
38  doz.  H  333  Kitchen  Forks,  13  inch 
36  doz.  H  334  Kitchen  Forks,  15  inch 
12  doz.  H  341  Perforated  Steel  Spoons 

8  doz.  H  691  Kitchen  Sets 

16  doz.  H  692  Kitchen  Sets 


24  X  54  doz. 

1.98 

22  X  39  doz. 

4.95 

23  X  52  doz. 

2.37| 

10x13  doz. 

.421 

doz. 

1     .86 

doz. 

.23 

doz. 

.27 

doz. 

.33 

doz. 

.19 

gross 

3.20 

doz. 

.84- 

doz. 

8.75 

doz. 

3.95 

RECORDING  PURCHASES  AND  SALES  201 

Marking  Goods 

163.  Method  of  Marking  Goods.  When  stock  is  placed  on  the 
shelves  in  the  salesroom,  the  cost  of  each  article  should  be  marked 
either  on  the  goods,  on  the  package  which  contains  them,  on  tags 
attached  to  the  goods,  or  on  card  lists  placed  near  the  goods. 

164.  Advantage  of  Marking.  In  some  lines  of  business  it  is 
necessary  to  have  the  selling  price,  or  both  the  cost  and  the  selling 
price,  marked  on  the  goods.  When  the  stock  becomes  low  and 
the  buyer  wishes  to  purchase  a  new  supply,  he  can  compare  the 
price  paid  for  the  goods  on  the  shelves,  with  quotations  of  prices 
made  to  him  by  the  salesmen  from  the  wholesale  houses.  It  would 
also  be  a  convenience  to  know  the  cost  of  an  article  if  it  proved  to 
be  a  slow  seller,  and  the  manager  determined  to  sell  at  a  reduced 
price  to  unload  the  stock.  One  of  the  chief  advantages  of  cost 
marking  is  in  taking  inventory  of  stock  and  finding  its  value  at 
cost  prices.  In  marking  goods,  the  cost  price  is  taken  from  the 
invoice. 

165.  "Blind  Price  Lists."  It  would  be  unwise  to  mark  the 
cost  in  figures,  as  this  would  disclose  the  cost  and  the  profit  to 
purchasers.  It  is,  therefore,  customary  for  merchants  to  adopt  a 
set  of  symbols,  called  a  cipher,  or  blind  price  list.  Any  symbols 
may  be  chosen,  but  they  will  be  more  easily  written  if  letters  are 
used,  and  these  letters  will  be  more  easily  remembered  if  they 
form  a  word  or  phrase.  The  word  or  phrase  selected  must  not 
contain  the  same  letter  twice.  Otherwise  the  same  letter  will 
represent  two  different  numbers. 

The  following  will  illustrate  : 

admonisher  mah 

1234567890  318 

Fitzaubrey  izy 

1  2  345  6  7  8  90  240 

166.  The  Repeater.  To  further  conceal  the  cost  a  "  repeater  " 
should  be  adopted.  When  the  same  figure  is  repeated,  as  in  f^l.55, 
the  repeater  sign  is  used  for  the  repeated  figure,     "x"  is  frequently 


202  RECORDING  PURCHASES  AND  SALES 

used  as  a  repeater,  but  because  it  is  so  commonly  used,  some  other 
repeater  would  perhaps  be  preferable.  Words  or  phrases  with 
eleven  letters  are  frequently  chosen  as  keys,  one  of  the  letters 
being  used  as  a  repeater. 

Using  "t"  as  the  repeater,  and  "admonisher"  as  the  key, 

$3.88  would  be  written  mht. 

Written  Work 

Using  "  blacksmith  "  as  the  key  word,  and  "  d  "  as  the  repeater, 
indicate  the  following  costs  : 

1.  $9.82.  2.  I   .09.  3.  $   .25.  4.  $  1.64. 

5.  11.00.  6.  16.20.  7.  I  .27.  8.  $  7.47. 

9.  $2.45.  10.  I   .55.  11.  11.33.  12.  $     .39. 

13.  18.23.  14.  15.00.  15.  il.17.  16.  112.47. 

17.  $6.62.  18.  $2.24.  19.  $   .36.  20.  $   1.44. 

Many  articles  are  bought  by  the  dozen  and  sold  by  the  piece. 
In  marking  goods  bought  in  this  way  it  is  necessary  to  divide 
the  cost  by  12.  This  division  will  be  facilitated  if  the  decimal 
equivalents  of  the  12ths,  from  -^^  to  \^  inclusive,  are  memorized. 

Make  such  a  table  of  equivalents  and  memorize  it.     Thus, 

Example.  What  is  the  cost  of  one  hat  at  the  rate  of  $29  a 
dozen  ? 

Solution.  /^  of  $  29  =  |  2^^  =  %  2.41f . 

Oral  Work 

What  is  the  cost  per  article  when  the  cost  per  dozen  is : 

1.  $27?         2.  $34?         3.  $64?         4.  $11?  5.  $  3.40? 

6.  $14.30?    7.  $7.50?      8.  $19.50?    9.  $46.60?    lo.  $37.40? 

167.  Showing  Cost  and  Selling  Price.  When  both  the  cost  price 
and  the  selling  price  are  shown,  it  is  customary  to  write  the  cost 
price  above  and  the  selling  price  below  a  line,  thus: 


RECORDING  PURCHASES  AND  SALES  203 

Cost  of  an  article,  §6.25. 
Selling  price,  18.00. 
Key  word,  Fitzaubrey. 
uia 


Price  mark, 


8.00 


Key  words  or  phrases  are  sometimes  used  to  mark  the  selling 
price  as  well  as  the  cost,  thus : 

Cost  key,  "  purchased  it " 

123456789  0       "  t "  is  the  repeater. 

Selling  key,  "  studying  her" 

12345678  90  "r"  is  the  repeater. 
Cost,  13.14. 

Selling  price,  f4.25. 

Mark,  4^. 
dty 

Written  Work 
Using  the  above  keys,  show  markings  for  the  following  : 

Cost  Selling  Price 

1.  $1.15  11.50 

2.  f   .65  $   .90 

3.  $1.30  il.75 

4.  $2.18  -  $2.50 

5.  $1.25  $2.60 

What  per  cent  of  profit  would  be  realized  from  selling  goods 
marked  as  follows,  using  "  purchased  it "  as  the  cost  key  and 
"  studying  her  "  as  the  selling  key  ? 

phi                     „      ah               -      „      dh                     ^      at 
6.     —rz'  7. 8. 9. 

1.75  ge  sty  ny 

Mark  the  cost  of  each  of  the  following  articles,  using  "  Now 
Pay  Quick  "  as  the  purchase  key.  , 

10.    $3.00  per  dozen.  li.    $  185.00  per  hundred. 

12.    $11.52  per  gross.  13.    $8.64  per  case  of  4  doz. 


204 


RECORDING  PURCHASES  AND  SALES 


Mark  both  the  cost  and  the  selling  price  of  the  following. 
Devise  a  cost  key  of  your  own,  and  mark  the  selling  price  by 
using  the  key  "importance." 

14.  Cost  i  2.60,  marked  to  gain  22  %. 

15.  Cost  •$  1.75,  marked  to  gain  18%. 

16.  Cost  $  25.00,  marked  to  gain  20%. 

The  following  is  a  list  of  key  words  and  phrases : 

Buy  for  Cash  Our  Last  Key  Equinoctial  Now  Be  Quick 

The  Big  Four  Republican  No  Suit  Case  You  Mark  His 

Black  Horse  Charleston  Frank  Smith  Now  Be  Sharp 

Buckingham  Bridgeport  Big  Factory  He  Saw  It  Run 

Authorizes  Cumberland  Don't  Be  Lazy  Hard  Moneys 

United  Cars  Dozen  Black  Market  Sign  What  Prices 

168.  Adding  the  Buying  Expenses  to  the  Cost  of  the  Goods.  Since 
the  buying  expenses  are  considered  a  part  of  the  cost  of  the  goods 
purchased,  many  merchants  add  a  portion  of  the  buying  expenses 
in  marking  the  cost  of  each  article.  Records  of  total  purchases 
and  buying  expenses  per  year  are  kept  for  several  years,  and  the 
average  per  cent  of  buying  expenses  is  determined,  as  shown  by 
the  following  illustration :  To  determine  a  rate  per  cent  of  buy- 
ing expenses  for  purchases  made  in  1915. 

1912,  Buying  Expenses,  $    785.75  Purchases,  $16,240.00 

1913,  Buying  Expenses,        835.50  Purchases,      19,360.00 

1914,  Buying  Expenses,        923.90  Purchases,      21,365.00 
Total  Buying  Expenses,  f  2545.15  Purchases,  156,965.00 

12545.15^  156,965.00  =  4.46^.%,  the  per  cent  of  buying  ex- 
penses. 

In  marking  costs,  4.4  %  of  the  cost  of  each  article  should  be 
added  as  buying  expenses. 

Note,    Probably  5  %  might  be  used  for  convenience. 

Written  Work 
1.    Compute  the  per  cent  of  buying  expenses  to  be  added  to 


the  wholesale  cost  of  goods  purchased  in  1916. 
to  the  nearest  whole  per  cent. 


Carry  the  result 


RECORDING  PURCHASES  AND  SALES  205 


Ybar 

Pttbchases 

Bitting  Expenses 

1913 

$10,246.80 

1534.50 

1914 

12,726.95 

592.90  ■ 

1915 

14,825.75 

615.45 

2.  Find  the  marked  cost  of  each  of  the  following  articles  after 
adding  the  baying  expenses.  Use  the  per  cent  of  buying  expenses 
found  in  Problem  1. 

a.  Wholesale  cost,  $16.20. 
h.  Wholesale  cost,  15.75. 
c.    Wholesale  cost,       2.35. 

3.  At  what  price  should  each  of  these  articles  be  sold  to  gain 
23  %  on  the  total  cost  including  buying  expenses  ? 

4.  The  purchases  made  by  a  store  in  1915  were  $3287.20; 
the  buying  expenses  for  the  same  year  were  %  327.90.  On  the  basis 
of  these  figures,  what  per  cent  should  be  added  for  buying  expenses 
on  purchases  made  in  1916  ?  Approximate  result  to  the  nearest 
per  cent. 

5.  What  objection  do  you  see  to  determining  a  per  cent  of 
buying  expenses  from  the  data  of  only  one  preceding  year  ? 

6.  Find  the  marked  cost  of  each  of  the  following  purchases, 
after  adding  the  per  cent  of  buying  expenses.  Use  the  per  cent 
of  buying  expenses  found  in  Problem  4. 

a.  Wholesale  cost,  %  2.45. 
h.  Wholesale  cost,  1.60. 
c.    Wholesale  cost,     34.50. 

7.  At  what  selling  price  should  each  of  the  articles  in  Prob- 
lem 6  be  marked  to  gain  16|  %  of  the  total  cost  ? 


CHAPTER  XVIII 
PAYING  FOR  GOODS 

169.  Making  Change.  The  payment  of  debts  between  persons 
in  the  same  community  is  usually  made  with  either  cash  or  checks. 
When  cash  is  the  medium  of  payment,  it  is  often  necessary  to 
"  make  change." 

Speed  and  accuracy  in  making  change  are  very  desirable.  The 
following  method  is  generally  used  by  experienced  tellers  and 
cashiers.  Beginning  with  the  amount  of  the  purchase,  take  from 
the  cash  drawer  enough  small  coins  to  bring  the  total  to  even 
dollars,  using  as  few  coins  as  possible,  then  take  out  dollars  or 
larger  denominations  until  the  total  equals  the  payment  made. 

Example.  A  five-dollar  bill  was  given  in  payment  for  a  pur- 
chase of  i.39.     How  should  change  be  made? 

Solution.     Take  1  penny, 

1  dime, 

1  fifty-cent  piece, 

4  dollars. 
As  a  check  on  the  accuracy  of  the  change,  say  as  you  give  the  customer  the 
money :  "  39  cents,  40,  50,  $  1,  $  5.00." 

Oral  Work 
Following  the  method  above,  state  what  coins  and  bills  should 
be  given  to  make  change  for  the  following  purchases,  using  the 
largest  denominations  possible ; 


Purchase 

Payment 

PURCHASK 

Payment 

1. 

$  .07 

$     .50 

2. 

$  .21 

$     .50 

3. 

«  .56 

$   1.00 

4. 

$  .63 

$  2.00 

5. 

$1.36, 

$  5.00 

6. 

$2.79 

$  5.00 

7. 

$3.66 

$  5.00 

8. 

$4.24 

$10.00 

9. 

$5.70 

$10.00 

10. 

$6.32 

$20.00 

11. 

$  .98 

$  5.00 

12. 

$2.77 

$10.00 

206 


PAYING  FOR  GOODS 


207 


PXTECHASB 

13.  $  3.46 
15.  $14.42 
17.    $11.13 


Payment 

$20.00 
$20.00 
$20.00 


Purchase 

Payment 

14.    $11.87 

$15.00 

16.    $  7.37 

$  8.00 

18.     $    1.13 

$20.00 

170.  Payments  by  Check.  The  payment  of  all  bills  by  the 
actual  transfer  of  money  would  be  so  inconvenient  that  the  giving 
of  checks  has  been  substituted,  and  it  is  said  that  about  90  %  of  all 
bills  are  now  paid  by  checks. 

171.  Deposits  and  Withdrawals.  Business  men  keep  the  greater 
part  of  their  cash  funds  on  deposit  in  banks  or  trust  companies. 
When  money  is  deposited,  a  deposit  slip  similar  to  the  illustration 
below  is  filled  out  by  the  depositor,  showing  his  name,  the  date, 
the  item,  and  the  amount  of  the  deposit. 


DEPOSITED  BY 

IN  THE 

STATE  BANK  OF  OAK  PARK 

OAK    PARK,    ILU. 

i 

nm.n 

DOLLARS 

H-0 

CENTS 
OO 

35 
00 

35 

snvKR 

7 
"6/ 

^IT.LS 

Total 

A  Deposit  Slip 

The  depositor,  wishing  to  pay  a  bill,  draws  a  check  ordering  the 
bank  to  pay  from  the  funds  on  deposit  the  sum  of  money  stated 
on  the  check  to  the  person  named  thereon.  If  the  depositor 
wishes  to  draw  cash  from  his  account,  he  may  make  the  check 
payable  to  "  Self  "  or  to  "  Cash." 


208  PAYING  FOR  GOODS 


70-1742 


OKDBR  OI'  /7L  Jt. LffiuL i^JSSlM— 


3'i^ixtnaj 


ruir 


DOIJ^ARS 


PAYABLE  IN  CHICAGO  EXCHANGC. 


C.  <^   QjtpAr(/n/ijor\) 


A  Check 

C.  L.  Stevenson,  the  drawer  of  this  check,  is  paying  M.  R.  Cole, 
\hQ  fayee^  f  15.65. 

Depositors  are  credited  by  the  bank  with  their  deposits,  and 
are  charged  with  the  checks  drawn  by  them.  Checks  received 
from  other  people  may  be  cashed  at  the  bank,  or  they  may  be 
deposited  the  same  as  cash.  All  checks  cashed  or  deposited  must 
be  indorsed ;  that  is,  they  mast  be  signed  on  the  hack  by  the  per- 
son cashing  or  depositing  them.  Checks  must  also  be  indorsed 
when  they  are  transferred  to  another  person  before  being  cashed 
at  the  bank.  Indorsement  should  be  made  on  the  back  of  the  left 
end  of  the  check. 


70-1742 


fOCf —  I>01iI<ARS 


C,  ^  .0teAj</nd'mJ 


A  Check  Indorsed 
M.  R.  Cole's  indorsement  before  cashing  the  check. 


PAYING    FOR    GOODS 


209 


New  Netherland  Bank 


^^, 


(EW 

DEPOSITC 


^ 


Indorsements 

172.  Blank  Indorsement.  This  form  of  indorsement  is  illus- 
trated on  the  back  of  the  check  on  page  208.  It  makes  the  check 
payable  to  bearer. 

173.  Indorsement  in  Full.     This  form  is  illustrated  below. 

Checks  indorsed  in  full  must  be  indorsed  by  the  new  owner 
before  being  cashed  ;  if  lost,  there  is  less  danger  of  their  being 
cashed  by  a  dislionest 
finder  than  if  they  were 
indorsed  in  blank. 

If  a  check,  note,  or 
draft  is  not  paid  by  the 
party  primarily  liable 
each  indorser  in  turn  be- 
comes responsible  for  its 
payment.  An  indorser 
may  limit  his  responsi- 
bility by  writing  the 
words  "without  re- 
course "  above  his  signa- 
ture. When  this  is  done, 
the  indorsement  is  said 
to  be  qualified. 

Written  Work 

1.  You  are  opening 
an  account  by  deposit- 
ing to-day  in  some  bank 
of  your  city,  gold,  15; 
silver,  12.25;  bills,  |7; 
and  the  three  following 


New  York ^^-^iZyC^^f^    /^/^ 


PLEASE  LIST  EACH  CHECK  SEPARATELY 


BILLS. 


GOLD_ 
SILVER 


CHECKS 


TataL 


DOLLARS 


/6 


^s^  :i3 


CENTS 


^J^-^ 


Deposit  Slip  Showing  Cash  and  Check 
Deposit 


210 


PAYING  FOR  GOODS 


checks :  1st,  drawn  by  Henry  Bailey  on  the  Merchants'  National 
Bank  of  Fargo,  North  Dakota,  amount  $26.30;  2d,  drawn  by 
W.  A.  Owen  on  the  Corn  Exchange  National  Bank  of  Chicago, 
amount  $8.35;  3d,  drawn  by  Frank  Mitchell  on  Carter's  Bank, 
Eldora,  Missouri,  amount  $12.40. 

Rule  a  deposit  slip  and  enter  this  deposit  properly. 

2.  On  a  blank  sheet  of  paper  draw  a  check  on  the  bank  in 
which  you  have  just  made  this  deposit,  paying  F.  G.  Benton 
128.25. 

What  is  your  balance  in  the  bank  after  drawing  this  check  ? 

3.  Seven  days  ago  you  bought  goods  from  F.  G.  Peterson, 
amounting  to  $28.50.  The  terms  of  the  invoice  were  2/10; 
N/30.     To-day  you  pay  the  bill  by  check.     Draw  the  check. 

What  is  your  balance  in  the  bank  ? 

174.  The  Check  Book.  Blank  checks  are  furnished  by  the  bank, 
bound  together  in  a  check  book.  Checks  are  usually  attached  to 
stubs,  on  which  are  recorded,  at  the  time  of  drawing  the  check,  its 
number,  the  date,  the  name  of  the  payee,  the  purpose  for  which  it 
was  given,  and  the  amount.  On  the  stub  there  is  also  kept  a 
record  of  the  balance  remaining  in  the  bank.  As  shown  by  the 
following  illustration,  a  balance  of  $186.80  was  brought  over 
from  May  10,  and  on  May  11  a  deposit  of  $68.35  was  made  and 
a  check  for  $4.80  was  drawn. 


Nft  ^ 


.%i£c=- 


Trot   ^=^Y-^^^i>^//,  y^^-s- 


MouTf  T  Vkrnou,  Iowa  ^ 


jLZ. VSISL   No_i^ 


Mount  Vernon  Bank 


.or  order  $4£l 


..so 

j1££_  Dollars 


Written  Work 

1.  Using  the  following  information,  rule  a  check  and  stub 
similar  to  the  preceding  illustration,  enter  the  necessary  facts,  and 
draw  the  check. 


PAYING  FOR  GOODS 


211 


Name  of  bank,  Fourth  National,  your  city. 

Balance  from  yesterday,  f  103.27.     Deposit  of  $  19.38. 

Check  No.  6,  drawn  by  you  to-day,  payable  to  G.  D.  Fitzgerald 
and  Co.,  in  payment  of  the  invoice  purchased  from  them  eight  days 
ago.     Amount  of  invoice,  873.28;  terms,  2/10;  N/60. 

Write  the  check  and  stub. 

What  is  the  new  balance  ? 

175.  The  Bank's  Accounts  with  its  Depositors.  All  banks  keep 
a  depositors'  ledger.  Usually  a  page  is  devoted  to  the  deposits  and 
checks  of  each  depositor. 


l/OHl/io'ifva'  %^  /i-a/i/oio^ 

DATE 

DEPOSITS 

CHECKS 

BALANCE 

/Cff.^ 

Un.. 

6 

/f<? 

6^^ 

1^3 

66 

^ 

^6 

^,^ 

"7 

i(-0 

(^ 

68 

60 

/,? 

p^") 

17^ 

7"^ 

16 

6 

HO 

/^ 

^0 

R 

75 

/i/.q 

HO 

^1 

6 

on 

/i,^ 

7^ 

/n^ 

7cl 

Cf 

3<9 

An  Account  in  a  Depositors'  Ledger 


Written  Work 

Rule  a  page  of  a  depositors'  ledger,  similar  to  the  preceding 
illustration,  and  enter  the  following  deposits  and  checks  made  by 
yourself,  computing  the  daily  balances.  In  computing  balances, 
use  the  method  of  adding  and  subtracting  explained  in  Section  13. 

March  2,  Deposit  1127.80.  March  3,  Check  126.14.  March  4, 
Check  123.19.  March  5,  Deposit  8114.32;  Check  f  12.19. 
March  6,  Checks  f  13.14,  $12.17.  March  10,  Deposits  132.76, 
f  22.14;  Check  117.14.  March  11,  Checks  126.19,  1127.14. 
March   13,   Deposits   112.19,   176.27;    Checks   $32.15,   127.19, 


212 


PAYING  FOR  GOODS 


113.81. 
127.93. 


March  16,  Deposit  1 27.94.      March  18,  Checks  S23.42, 


176.  The  Clearing  House.  Any  bank  will  cash  the  checks 
drawn  on  other  banks,  provided  the  person  presenting  them  is 
known  at  the  bank  or  is  properly  identified.  For  example,  if  you 
are  given  a  check  on  the  First  National  Bank,  you  can  cash  it  or 
deposit  it  at  the  Second  National  Bank.  The  Second  National 
then  collects  the  amount  of  the  check  from  the  First  National. 

When  there  are  several  banks  in  the  same  city,  the  checks  are 
collected  through  a  Clearing  House.  The  representatives  of  the 
various  banks  meet  at  the  Clearing  House,  bringing  the  checks 
which  they  have  paid  for  other  banks.  Each  bank  is  credited  with 
the  amount  of  the  checks  which  it  has  paid  for  other  banks,  and 
debited  with  the  amount  of  the  checks  which  all  other  banks 
have  paid  for  it.  The  Clearing  House  collects  from  those  having 
debit  balances  and  pays  those  having  credit  balances. 

Let  us  suppose  that  there  are  three  banks  in  a  city:  the  First 
National,  the  First  State,  and  the  City  National.  The  repre- 
sentatives will  meet,  each  bringing  the  checks  paid  by  his  bank 
for  the  other  banks  the  preceding  day,  and  a  sheet  showing  the 
amount  paid  for  each  of  the  other  banks.  The  statements  brought 
by  the  representatives  of  the  banks  are  shown  below : 

First  National 


Paid  for 

Amount 

First  State 

$16,265.00 

12,146.80 

Total       .     .     . 

$28,411.80 

First  State 

Paid  for 

Amount; 

Kirst  National                     .                .     .           

$   8,368.28 

City  National     . 

0,208.48 

Total      .     . 

$17,576.76 

PAYING  FOR  GOODS 
City  National 

213 

Paid  for 

Amount 

Fir.st  National 

$12,875.00 
4,738.80 

First  State 

1 

Total       .     .     . 

S  17.613  80 

At  the  Clearing  House  a  sheet  similar  to  the  following  is  pre- 
pared. In  the  debit  column  is  placed  the  total  value  of  checks 
paid /or  each  bank;  in  the  credit  column  is  placed  the  total  value 
of  checks  paid  hy  each  bank.  The  balance  columns  show  the 
balances  payable  by  or  to  each  bank. 

Manager's  Sheet 


Bank 

Debits 

Credits 

Debit  Balance 

Credit  Balance 

First  National     .     . 
First  State      .     . 
City  National      .     . 

$21,243.28 
21,003.80 
21,355.28 

$28,411.80 
17,576.76 
17,613.80 

$63,602.36 

$3427.04 
3741.48 

$7168.52 

Totals     .... 

$63,602.36 

$7168.52 

$7168.52 

The  First  State  and  the  City  National'  each  turns  over  to  the 
Clearing  House  the  amount  of  its  debit  balance  ;  the  Clearing 
House  pays  this  amount  to  the  First  National.  In  this  way  pay- 
ment of  over  sixty-three  thousand  dollars  is  made  by  the  actual 
transfer  of  only  a  little  more  than  seven  thousand  dollars. 

Written  Work 

Prepare  a  Manager's  Sheet,  and  find  the  debit  or  credit  balance 
of  each  bank  in  the  following  Clearing  House  Association.  The 
amount  of  the  checks  paid  by  each  bank  is  shown  by  the  debit 
sheets  which  follow. 

Harper's  State  Bank 

Paid  fob  .  Amount 

Harper's  State 

First  National  $23,756.27 

Traders'  14,259.95 

Merchants'  National  25,726.87 

Farmers'  &  Mechanics  9,243.65 

.       First  State  12,060.26 


214 


PAYING  FOR  GOODS 


First  National  Bank 


Paid  foe 

Amount 

Harper's  State 

$13,263.37 

First  National 

Traders' 

8,836.39 

Merchants'  National 

14,856.74 

Farmers'  &  Mechanics 

8,345.93 

First  State 

8,325.57 

Traders'  Bank 

Paid  fob 

Amount 

Harper's  State 

15,273.85 

First  National 

12,573.82 

Traders' 

Merchants'  National 

7,252.55 

Farmers'  &  Mechanics 

11,257.37 

First  State 

10,456.25 

Merchants'  National 

Paid  foe 

Amount 

Harper's  State 

13,123.64 

First  National 

6,027.30 

Traders' 

10,936.40 

Merchants'  National 

Farmers'  &  Mechanics 

7,238.37 

First  State 

9,235.35 

Farmers'  &  Mechanics 

Paid  foe 

Amount 

Harpers'  State 

$2,346.75 

First  National 

5,236.73 

Traders' 

4,232.25 

Merchants'  National 

7,727.86 

Farmers'  &  Mechanics 

First  State 

2,005.39 

PAYING  FOR  GOODS  215 


First 

State 

Paid  for 

Amount 

Harper's  State 

18,946.27 

First  National 

1,856.23 

Traders' 

11,472.75 

Merchants'  National 

923.88 

Farmers'  &  Mechanics 

2,423.73 

First  State 

Which  banks  will  pay  to  the  Clearing  House,  and  how  much 
will  each  pay? 

Which  banks  will  receive  from  the  Clearing  House,  and  how 
much  will  each  receive  ? 

177.  Exchange  on  Checks.  Checks  are  frequently  used  to  send 
money  to  people  in  cities  other  than  the  one  in  which  the  drawer 
of  the  check  resides.  For  example,  if  you  have  money  deposited 
in  the  Home  National  Bank  of  your  city,  you  may  draw  a  check 
against  this  deposit  and  send  it  to  Mr.  Perkins  of  Omaha.  Mr. 
Perkins  will  take  it  to  his  bank  in  Omaha,  which  will  pay  the 
check,  even  though  it  has  no  knowledge  of  you  or  your  de- 
posit in  the  Home  National  Bank.  The  fact  that  Mr.  Perkins 
is  known  at  his  bank,  and  that  he  agrees  to  refund  the  money 
if  the  check  proves  worthless,  is  sufficient  protection  for  his 
bank. 

When  banks- pay  out-of-town  checks,  they  incur  a  certain  amount 
of  expense  in  collecting  them.  To  cover  this  expense  they  often 
require  persons  for  whom  they  cash  checks  to  pay  them 
"  Exchange."  When  exchange  is  charged,  a  common  rate  is  ^^^  of 
one  per  cent  of  the  face  of  the  check,  with  a  minimum  charge  of 
from  10  cents  to  25  cents. 

Example.  Mr.  Black,  who  lives  in  Bloomington,  Illinois, 
received  two  checks  in  his  mail.  One  was  from  Wm.  Harris, 
of  Lincoln,  Nebraska,  for  $365.85;  the  other  from  H.  B.  Felter, 
of  Cincinnati,  Ohio,  for  #28.25.  The  bank  at  which  Mr.  Black 
cashed  these  checks  charges  for  exchange  -^^  %  of  the  face  of  each 


216  PAYING  FOR  GOODS 

check,  or  a  minimum  of   10  cents.     What  was  the  exchange  on 
the  checks  ? 

Solution.  tV  %  of  ^  365.85  =  $  .37. 

tV%  of  $28.25  =  1.028. 
Since  $  .028  is  below  the  minimum,  10  cents  exchange  is  charged. 
The  total  exchange  is  f  .47. 

Written  Work 
Prepare  deposit  tickets  for  the  following: 

1.  Deposited  by  Wm.  Frend,  of  Peoria,  Illinois,  in  the  Peoria 
State  Bank,  on  August  7,  1915 : 

Gold,  ^25;  silver,  137.50;  currency,  1 17;  and  checks  as 
follows : 

Check  drawn  by  D.  P.  Snyder  of  Amboy,  Illinois,  $65.75. 
Check  drawn  by  Hammond  &  Davis  of  Lima,  Iowa,  $236.57. 
Check  drawn  by  B.  J.  Harris  of  Springfield,  Illinois,  $235. 
The  bank  charges  r^-^  %  exchange.     Minimum,  15  cents. 
Find  the  total  of  the  items  and  deduct  the  charge  for  collection. 

2.  Deposited  by  G.  D.  Bernham  of  Hawkeye,  Iowa,  in  the 
Hawkeye  State  Bank,  on  August  20,  1915. 

Check  drawn  by  S.  Y.  Benton  of  Clarinda,  Iowa,  $75.88. 
Check  drawn  by  D.  W.  Galbreath  of  Morris,  Illinois,  $57.93. 
Check  drawn  by  F.  J.  Ressler  of  Pasadena,  California,  $346.49. 
Check  drawn  by  D.  T.  Bailey  of  Buffalo,  New  York,  $48.95. 
The  bank  charges  exchange  on  the  California  and  New  York 
checks;  rate,  -^-^  %,  minimum  25  cents  each. 

Note.  It  is  the  custom  of  some  banks  to  cash  checks  on  banks  in  near-by  states 
without  charging  exchange. 

178.  Certified  Checks.  If  you  wish  to  assure  the  person  to 
whom  you  send  a  check  that  you  have  sufficient  money  in  the 
bank  to  pay  the  check,  you  may  have  the  check  certified.  Draw 
the  check  in  the  usual  way  and  take  it  to  your  bank.  The 
cashier  will  write  "Accepted"  or  "Certified"  or  "Good"  across 
its  face  and  will  sign  his  name.  He  will  then  set  aside  from 
your  deposit  the  amount  of  the  check,  holding  it  in  the  bank's 
funds  until   the  check  is  presented  for  payment.     Certifying  the 


PAYING  FOR  GOODS  217 

check  reduces  the  receiver's  risk  of  cashing  a  worthless  check, 
but  it  does  not  relieve  him  from  a  possible  exchange  fee. 


Waseca.Minn 


^zJjz/U:. 


•The  First  Nati ox. 


A  Certified  Check 

179.  Bank  Drafts.  Banks  keep  funds  on  deposit  in  the  banks 
of  the  larger  cities,  and  draw  checks  on  these  city  banks  just 
as  you  may  draw  a  check  on  the  bank  in  which  you  have  deposited 
money.  An  order  drawn  by  one  bank  against  its  deposit  in 
another  bank  is  called  a  "Bank  Draft." 

180.  Advantages  of  Bank  Drafts.  A  bank  draft  is  preferable  to 
a  check  when  sending  money  from  one  town  to  another,  for  two 
reasons  : 

a.  The  draft  is  drawn  by  a  bank,  while  the  check  is  drawn  by 
an  individual.  There  is  therefore  a  greater  certainty  that  the 
bank  draft  is  genuine,  and  will  be  paid  when  presented. 


X  Sta^xe  Bi%j^rK  or  Ei 


xn  39887 


Rot  TO  THE  OBDEROfF^ 


^ 


TO  NATIONAL  BANK  OF  THE  REPUBUC    )  /\~-/^ /^  •  ^ 

M3  CHICAGO.  ILLINOIS  J  ^^^- / ^~^-^^/^L^tj2yyiyU>i^ 


A  Bane  Draft 


218  PAYING  FOR  GOODS 

h.  Bank  drafts  are  drawn  on  banks  in  large  cities,  while  checks 
may  be  drawn  on  banks  in  small  towns.  There  is  less  expense, 
therefore,  incurred  in  collecting  a  bank  draft  than  in  collecting  a 
check,  and  banks  seldom  charge  exchange  when  cashing  bank 
drafts. 

Explanation.  D.  B.  Carpenter  is  the  cashier  of  the  State 
Bank  of  Eudora.  This  bank  has  funds  on  deposit  in  the  National 
Bank  of  the  Republic,  Chicago.  When  the  National  Bank  of  the 
Republic  pays  this  draft,  it  will  deduct  the  amount  from  the  bal- 
ance of  the  Eudora  Bank. 

S.  F.  Simonds  lived  in  Eudora  and  wished  to  send  i  16.25  to 
F.  E.  Craig  of  Bloomington,  Illinois.  When  he  purchased  the 
draft  from  his  bank,  he  had  it  made  payable  to  himself.  He 
might  have  had  it  made  payable  to  F.  E.  Craig,  but  if  he  had 
done  so,  his  (Simonds's)  name  would  not  have  appeared  on  the 
draft,  and  if  it  had  become  separated  from  the  letter  accompany- 
ing it,  Craig  might  have  had  difficulty  in  telling  from  whom  he 
received  it. 

After  receiving  the  draft,  Simonds  indorsed  it  as  follows; 

Pay  to  the  order  of 

F.  E.  Craig. 

S.  F.  Simonds. 

and  sent  it  to  Mr.  Craig. 

Mr.  Craig  indorsed  it  and  cashed  it  at  the  Corn  Belt  National 
Bank  of  Bloomington. 

We  will  now  follow  the  steps  by  which  the  Corn  Belt  National 
collected  the  draft.  This  bank  deposits  funds  with  the  Conti- 
nental National  Bank  of  Chicago,  which  is  called  its  "corre- 
spondent," and  it  therefore  sent  this  draft,  with  others  paid  the 
same  day,  to  the  Continental  National  bank  as  a  deposit. 

The  Continental  National  sent  the  draft  to  the  Clearing  House, 
which  collected  it  from  the  National  Bank  of  the  Republic. 

After  paying  the  draft,  the  National  Bank  of  the  Republic 
charged  the  amount  to  the  State  Bank  of  Eudora. 


PAYING  FOR  GOODS 


219 


The  preceding  statement  may  be  summarized  as  follows : 


State  Bank  of  Eudora  sells 
the  draft  to 

S.  F.  Simonds,  who  paid  for 
it  either  with  cash  or 
a  check ;  and  sent  it  to 


I 


F. 


E.  Craig,  who  gave 
Simonds  credit  for 
il6.25;  and  deposited 
the  draft  at 


I 


Bloomington  Bank,  which 
gave  Craig  $  16.25 ; 
and  sent  the  draft  to 


Continental  National,  which 
gave  the  Bloomington 
Bank  credit  for  $16.25; 
and  collected  the  draft 
through  the  Clearing 
House  from 

I 

National  Bank  of  the  Repub- 
lic, which  paid  the 
Continental  National 
$16.25,  and  charged 
Eudora  Bank  116.25. 


Indorsements  on  the  Model  Bank 
Draft 


^    ^  ^-^>«e..^ 


J^  £.  (yi^^^j^^ 


Pay  to  the  order  of 
Continental  National  Bank. 

All  prior  indorsements  guaranteed. 
Corn  Belt  National  Bank, 
Bloomington,  III., 
F.  A.  Frend,  Cashier. 


Pay  to  the  order  of 
Any  Bank,  Banker,  or  Trust  Co. 

Prior  indorsements  guaranteed. 

July  12,  1915. 
Continental  National  Bank, 
M.  B.  Jones,  Cashier. 


These  indorsements  indicate  the 
successive  owners  of  the  draft.  The 
last  two  indorsements  are  made  with 
rubber  stamps.  The  last  one  is  made 
payable  to  "any  Bank,  Banker,  or 
Trust  Company,"  for  convenience 
in  collecting  through  the  Clearing 
House. 


220  PAYING  FOR  GOODS 

181.  The  Cost  of  Bank  Drafts.  When  a  bank  sells  a  draft,  it 
gives  the  purchaser  the  benefit  of  its  deposit  relations  with  a  large 
city  bank.  For  this  convenience  it  may  make  a  charge  called 
"Exchange."  It  will  be  noted  that  exchange  on  a  check  is  paid 
by  the  person  receiving  and  cashing  it,  while  the  exchange  on  a 
draft  is  paid  by  the  person  purchasing  and  sending  it.  When  ex- 
change is  charged,  -^-^^o  with  a  minimum  of  10  cents  is  a  custom- 
ary fee. 

The  following  is  a  copy  of  the  check  given  by  S.  F.  Simonds  to 
the  State  Bank  of  Eudora  to  pay  for  the  draft  purchased.  There 
was  a  charge  of  10  cents  for  exchange. 


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Written  Work 

1.  You  owe  H.  J.  Palmer,  of  Toledo,  Ohio,  $  27.35.  You  buy 
a  draft,  payable  to  yourself  for  this  amount,  from  the  Merchants' 
State  Bank  of  your  city,  of  which  A.  R.  Burton  is  the  cashier. 
The  draft  is  drawn  on  the  Home  National  Bank  of  New  York 
City.     Exchange,  10  cents.     Draft  is  made  payable  to  you. 

Write  a  draft  similar  to  the  one  which  the  bank  would  give  you, 
and  the  check  which  you  would  give  the  bank  in  payment. 
Indorse  the  draft.     How  soon  can  Mr.  Palmer  get  his  money  ? 

2.  Mr.  Palmer  cashed  the  draft  at  the  High  Street  National  Bank 
of  Toledo,  B.  F.  Ohren,  Cashier.  The  High  Street  National  sent  it 
to  the  Bankers'  National  Bank  of  New  York,  G.  B.  Martin,  Cashier. 

The  Bankers'  National  collected  it  through  the  Clearing  House. 
Show  the  indorsements  on  the  draft. 


PAYING  FOR  GOODS 


221 


3.  Find  the  cost  of  a  draft  sent  to  pay  an  invoice  of  i  246.50, 
less  a  cash  discount  of  2  %.  Exchange,  ^  %  of  the  face  of  the 
draft;   minimum,  15  cents. 

4.  On  October  8,  you  purchased  from  Benedict  &  Meredith, 
Pittsburgh,  Pennsylvania,  an  invoice  amounting  to  $794.86. 
Terms,  2/15 ;  N/60.  On  October  16,  you  paid  the  invoice  by  a 
draft  purchased  at  the  Claim  Street  State  Bank  of  your  city,  J. 
D.  Haines,  Cashier.  The  draft  was  drawn  on  the  First  National 
Bank  of  New  York.     Exchange,  ^3^  %. 

Write  the  draft  which  you  received,  the  indorsement,  and  the 
check  you  gave  to  pay  for  the  draft. 

182.  Postal  Money  Orders.  A  postal  money  order  is  an  order 
drawn  by  one  postmaster  on  the  postmaster  at  some  other  office, 
calling  for  the  payment  of  a  stated  sum  of  money  to  the  person 
named  on  the  order.  Postal  money  orders  are  commonly  used  to 
make  payments  by  mail.  They  are  issued  in  any  amount  from  $.01 
to  $100.00.  As  a  means  of  protection,  no  order  is  issued  for  more 
than  $100.00.  If  it  is  desired  to  send  more  than  this  amount, 
additional  orders  may  be  purchased. 

Fees  for  money  orders  paj^able  in  the  United  States  (which  in- 
cludes Hawaii  and  Porto  Rico)  and  its  possessions,  comprising  the 
Canal  Zone,  Guam,  the  Philippines,  as  well  as  in  Bermuda,  British 
Guiana,  British  Honduras,  Canada,  Cuba,  Mexico,  Newfoundland, 
at  the  United  States  Postal  Agency  in  Shanghai  (China),  in  the 
Bahama  Islands,  and  in  certain  other  islands  in  the  West  Indies, 
are  as  follows : 


from  $    0.01  to  $ 

2.50    . 

3  cents 

from       2.51  to 

5.00    . 

5  cents 

from       5.01  to 

10.00    . 

8  cents 

from     10.01  to 

20.00    . 

10  cents 

from     20.01  to 

80.00    . 

12  cents 

from     30.01  to 

40.00    . 

15  cents 

from     40.01  to 

50.00    . 

18  cents 

from     50.01  to 

60.00    . 

20  cents 

from     60.01  to 

75.00    . 

.     25  cents 

from     75.01  to 

100.00    . 

.     30  cent? 

222  PAYING  FOR  GOODS 

Examples.     1.    What  is  the  cost  of  an  order  for  $27.35  ? 
Solution.    $27.35  lies  between  $20.01  and  $30.00,  and  the  rate  is  12  cents. 
Total  cost  of  order,  $27.35  +  .12  =  $27.47. 

2.    What  is  the  cost  of  sending  $  267.95  by  postal  money  orders  ? 

Solution.  Two  orders  for  $100.00  each,  and  one  order  for  $67.95,  will  be 
purchased. 

Fees  of  two  $100.00  orders,  60  cents. 

Fee  of  $67.95  order,  25  cents. 

Total  fees,  85  cents. 

Total  cost  of  orders,  $267.95  +  .85  =  $268.80. 

183.  Bank  Drafts  and  Postal  Money  Orders  Contrasted.  Note  the 
following  differences  between  a  bank  draft  and  a  postal  money 
order : 

A  bank  draft  may  be  indorsed  as  many  times  as  desired. 

A  postal  money  order  may  be  indorsed  only  once. 

A  bank  draft  may  be  cashed  at  any  bank. 

A  postal  money  order  must  be  presented  to  the  post  office  on 
which  it  is  drawn,  or  to  a  bank  which  can  cash  it  at  that  post 
office. 

A  bank  draft  is  payable  as  soon  as  it  is  presented  to  a  bank. 

At  the  time  of  issuing  a  money  order  the  issuing  postmaster 
sends  a  notice  to  the  paying  postmaster.  A  postal  money  order 
will  not  be  paid  until  the  paying  office  has  received  this  notice. 
However,  this  does  not  usually  cause  any  delay. 

184.  Express  Money  Orders.  Express  money  orders  are  similar 
in  many  respects  to  postal  money  orders.  They  can  be  purchased 
from  the  agent  of  the  express  company,  and  are  payable  from  the 
funds  of  the  express  company  on  deposit  in  various  banks  specified 
in  the  order. 

No  order  is  issued  for  an  amount  larger  than  $30.  If  it  is  desired 
to  send  a  larger  amount,  additional  orders  must  be  purchased. 

Express  Money  Order  Rates.  The  rates  for  express  money 
orders  are  the  same  as  for  postal  money  orders,  although  no  order 
is  issued  for  more  than  $50. 

Example.  What  will  be  the  total  fee  for  the  transfer  of  8241.75 
by  express  money  orders  ? 


PAYING  FOR  GOODS  223 

Solution.  Four  $50  orders  at  the  rate  of  30  cents  per  hundred  will  cost 
60  cents. 

One  order  for  $41.75  will  cost  18  cents.     Total,  78  cents. 

185.  Telegraph  Money  Transfers.  Money  may  be  transferred 
by  telegraph  when  there  is  an  urgent  necessity  for  immediate 
payment.  The  rates  for  this  service  between  points  in  the 
United  States  are  determined  as  follows : 

To  the  tolls  for  a  fifteen-word  message  between  the  office  of 
deposit  and  the  office  of  payment  add  the  following  charges: 
For  1 25.00  or  less  ....     25  cents 

25.01  up  to  150     .     .     .     .     35  cents 
50.01  up  to     75     ....     60  cents 
75.01  up  to  100     .     .     .     .     85  cents 
For  amounts  above  §100  add  (to  the  f  100  rate)  25  cents  per 
hundred  (or  any  part  of  ilOO)  up  to  13000. 

For  amounts  above  §3000  add  (to  the  §3000  rate)  20  cents  per 
hundred  (or  any  part  of  §100). 

Exam'ples.  1.  What  is  the  charge  for  sending  §25  or  less  to  a 
point  where  the  fifteen-word  rate  is  65  cents  ? 

Solution.  $  .25  Minimum  charge 

.65  Tolls  on  15-word  message 
$  .90  Total  charge 

2.  What  is  the  total  charge  for  transfer  of  §105  if  the  tolls 
on  a  fifteen-word  message  are  65  cents  ? 

Solution.  |  .85  Charge  for  first  $  100 

.25  Charge  for  fraction  of  second  $  100 
.65  Tolls  on  15-word  message 
$1.75  Total  rate 

Written  Work 
1.    Assuming  that  you  owe  the  following  bills: 
F.  G.  Young,     §39.40; 
P.  S.  Sanborn,  §112.75; 
H.  L.  Colwell,  §416.25,  less  3%; 
determine  the  fees  for  the  purchase  of  either  postal  or  express 
money  orders  for  transferring  money  to  make  payments.     Com- 
plete the  following  blank  form. 


224 


PAYING  FOR  GOODS 


Namb 


Net  Amount 
OF  Bills 


Fees  for 
Money 
Orders 


Total  Cost 


Denomina- 
tions of 
Orders 
Received 
FROM  Ex.  Co. 


Denomina 

tions  of 

Orders 

Received 

from  P.O. 


2.  What  is  the  charge  for  a  telegraph  money  transfer  of  $23.15 
to  a  point  where  the  fifteen- word  message  rate  is  85  cents  ? 

3.  What  is  the  charge  for  a  telegraph  money  transfer  of  $52,85 
to  a  point  where  the  fifteen- word  message  rate  is  $1.30? 

4.  What  is  the  total  cost  of  a  telegraph   money  transfer   for 
$215  to  a  point  where  the  fifteen- word  rate  is  65  cents  ? 


CHAPTER   XIX 
COLLECTING    BILLS 

186.    Statements.     At  periodical  intervals,  usually  on  the  first 
day  of  each  month,  merchants  send  a  statement  to  their  customers. 


STATEMENT 

ACCOUNT  NO. 

5422 

WEBSTER  &  MCCLELLAN 

16  JEFFERSON  STREET 

F.  B.  Turner,                                                                   CHICAGO,   May  1 , 

La  Grange,  111.. 

1915 

Airbills  are  due  the  fint  of  the  month  after  purchase. 

This  statement  Is  Intended  to  show  you  the  condition  of  your  account  on  our  books.    If  this  statement  does  not  correspond  with 
your  accounts  please  notify  us.  If  correct,  please  remit. 

To  balance,  as  per  former  statement 

17.65 

To.Mdse,  as  per  invoice 

Apr  11^3 

23.78 

April  15 

19.65 

April  23 

Credits 

27.84 

88.92 

April  20 

By  Udse  returned 

.      2.85 

April  26 

By  Cash 

75.00 

77.85 

Balance 

11.07 

This  statement  shows  the  date  and  amount  of  each  purchase,  the 
date  and  amount  of  each  payment,  and  the  balance  due.  The 
items  sold  are  not  enumerated  in  the  above  statement  because 
the  invoices  ma}^  be  consulted  to  obtain  this  information. 

225 


226 


COLLECTING  BILLS 


HENDERSON  &  BISHOP 

143  WEST  MONROE  AVENUE 

R.  F.  Bailey 

West  Union,  Iowa. 

CHICAGO.    July  1 

,    19  15 

Intereet  charged  on  overdue  aooounti. 

All  claims  for  correction  must  be  made  on  receipt  of  statement  > 

DATE 

ITEM 

DEBIT 

CREDIT 

BALANCE 

June  1 

Balance,  May  31 

75.60 

June  2 

Cash 

75.00 

.60 

June  5 

Mdse 

34.55 

•35  .15 

June  11 

Mdse 

17.26 

52.41 

June  15 

Returned  goods 

4.35 

48.06 

June  24 

Mdse 

5.96 

54.02 

Another  Form  of  Statement 


Written  Work 

1.  Rule  a  statement  similar  to  the  first  illustration,  and  enter  the 
following :  Your  transactions  with  S.  J.  Smith,  Fayette,  Missouri. 

Balance,  August  1,  1127.86. 

Purchases,  August  3,  172.85  ;  August  11,  $23.89  ;  August  14, 
$75.23;  August  20,  1 14.76  ;  August  28,  I  38.97. 

Payments,  August  2,  Cash  f  126. 00;  August  13,  Returned 
merchandise,  $15.00. 

Statement  rendered  September  1. 

2.  Rule  a  statement  similar  to  the  second  illustration,  and  enter 
the  following  transactions  with  Beardsley  &  Russel,  Montgomery, 
Alabama. 

Balance,  October  1,  1915,  $32.11. 

Purchases,  October  5,  $45.89;  October  9,  $23.87  ;  October  12, 
$243.87;  October  15,  $65.00;  October  21,  $52.57;  October  26, 
$40.50  ;  October  29,  $50.25. 


COLLECTING  BILLS  227 

Payments,  October  7,  150.00;  October  21,  J^  125.00;  October 
24,  $40.00. 

Returned  merchandise,  October  20,  $5.50. 
Statement  rendered  November  1. 

187.  Commercial  Drafts.  Commercial  drafts  offer  an  effective 
method  of  collecting  accounts.  A  commercial  draft  is  an  order 
drawn  by  the  party  to  whom  money  is  due,  requesting  the  debtor 
to  pay  a  stated  sum  of  money  either  to  the  drawer  of  the  draft  or 
to  a  third  party  mentioned  in  the  draft. 

Two  and  Three  Party  Drafts.  If  a  draft  requests  the  debtor  to 
pay  money  to  the  drawer,  it  is  called  a  two-party  draft.  Such 
drafts  are  collected  through  a  bank. 

If  a  draft  requests  the  debtor  to  pay  money  to  a  third  party,  it 
is  called  a  three-party  draft. 

Sight  and  Time  Drafts.  If  a  draft  requests  immediate  payment, 
it  is  called  a  sight  draft.  Such  a  draft  is  payable  at  once,  without 
acceptance. 

If  a  draft  is  to  be  paid  after  a  stated  time,  it  is  called  a.  time 
draft. 

188.  Parties  to  a  Draft.  The  drawer  is  the  person  who  draws  the 
draft.  The  drawee  is  the  person  on  whom  the  draft  is  drawn, 
and  who  is  requested  to  pay  the  money.  The  payee  is  the  person 
to  whom  the  money  is  to  be  paid.  In  case  of  a  two-party  draft, 
the  drawer  is  also  the  payee. 

189.  Reasons  for  Drawing  Drafts. 

(a)  To  effect  prompt  payment  of  invoices. 

1.  How  a  sight  draft  is  used  :  Wholesale  houses  often  make 
terms  similar  to  the  following  :  ''  Sight  draft  in  ten  days,  less 
2  %."  At  the  expiration  of  ten  days  from  the  date  of  sale,  the 
selling  merchant  sends  a  sight  draft  for  the  net  amount  of  the 
bill,  to  the  purchasing  merchant's  bank.  The  bank  presents  it 
to  the  purchaser  for  collection. 

2.  How  a  time  draft  is  used  :  If  the  terms  of  the  sale  were 
"  Thirty-day  draft,"  the  selling  merchant  would,  at  the  time  of 


228  COLLECTING  BILLS 

making  the  sale,  draw  a  thirty- day  draft  on  the  purchaser  and 
send  it  to  him  for  acceptance.  After  the  draft  has  been  accepted, 
it  has  the  same  value  as  a  note  because  the  purchaser  has  agreed 
to  pay  it  when  due.  The  seller  may  borrow  money  from  a  bank, 
giving  the  accepted  draft  as  security. 

(5)  As  a  means  of  collection.  When  a  bill  is  overdue,  and  the 
debtor  is  slow  in  making  settlement,  a  draft,  to  be  collected  by  his 
bank,  will  often  bring  about  a  settlement. 

((?)  To  make  C.  O.  D.  shipments  by  freight.  When  a  mer- 
chant sells  goods  to  be  shipped  by  freight,  he  receives  a  bill  of 
lading  from  the  railroad  company.  This  bill  of  lading  is  the 
railroad's  receipt  for  the  goods.  To  make  a  C.  O.  D.  shipment 
the  seller  obtains  an  Order  Bill  of  Lading  from  the  railroad. 
The  purchaser  cannot  get  the  goods  from  the  railroad  without 
surrendering  the  bill  of  lading.  Therefore,  a  selling  merchant, 
instead  of  sending  the  bill  of  lading  direct  to  the  purchaser, 
attaches  it  to  a  sight  draft  and  sends  the  draft  and  the  bill  of 
lading  to  a  bank  in  the  purchaser's  town. 

In  order  to  get  the  goods  the  purchaser  must  have  the  bill  of 
lading  ;  in  order  to  get  the  bill  of  lading  he  must  pay  the  draft 
at  the  bank. 

(c?)  To  avoid  the  transfer  of  money.     If 

Jones  owes  Smith,  and 
Smith  owes  Brown, 

Smith  may  collect  the  debt  from  Jones  and  pay  his  own  debt  to 
Brown,  or  he  may  request  Jones  to  send  the  money  direct  to 
Brown.  If  Jones  and  Brown  live  in  the  same  town,  both  debts 
can  be  paid  without  sending  the  funds  through  the  mail,  even 
though  Smith  lives  in  a  distant  city.  A  three-party  draft  is  used 
for  this  purpose,  Smith  requesting  Jones  to  pay  Brown. 

190.  Two-party  Sight  Draft.  Benjamin  Osborne  of  Madison, 
Kansas,  owes  J.  B.  Dunham  of  Toledo,  Wisconsin,  8  28.65.  In 
order  to  collect  this  bill,  Mr.  Dunham  draws  the  following  draft 
on  Mr.  Osborne. 


COLLECTING  BILLS  229 


<LZcCf~CylitZf  .g^^:</^  Oyn^    -Too 


(6e^Aecesa^ed^ya9teC'yC^a4^a€yM€^/i/r/m€^, 


Mr.  Dunham  then  indorses  the  draft  as  follows: 

Pay  to  the  order  of 
The  First  State  Bank  of  Toledo 
for  collection  only. 
J.  B.  Dunham. 

and  gives  it  to  his  bank  to  collect. 

The  bank,  in  turn,  indorses  it  as  follows  : 

Pay  to  the  order  of 

The  Farmers  National  Bank  of  Madison 

for  collection  only. 

First  State  Bank, 

Toledo,  Wisconsin, 

E.  J.  Baxter,  Cashier. 

and  forwards  it  to  the  bank  at  Madison  to  collect.  The  Madison 
bank  presents  it  to  Mr.  Osborne  for  payment.  Mr.  Osborne  is 
not  obliged  to  pay  this  draft,  but  if  he  owes  the  bill,  he  will  proba- 
bly do  so  in  order  to  keep  his  standing  good  at  his  bank. 

If  Osborne  pays  the  draft,  the  bank  stamps  a  receipt  thereon, 
and  gives  the  draft  to  Osborne.  The  bank  keeps  a  certain  amount 
as  a  collection  fee,  and  returns  the  balance  to  the  bank  at  Toledo, 
where  Mr.  Dunham  receives  the  proceeds  in  cash  or  as  a  deposit 
credit. 

If  Osborne  does  not  pay  the  draft,  it  is  returned  to  the  bank  at 
Toledo  with  a  statement  of  the  reason  for  non-payment. 


230 


COLLECTING  BILLS 


191.    Rates  for  Collecting  Drafts.     ''Collection"  rates,  like  ex- 
change rates,  differ.     A  common  rate  is  -^-^  %,  with  a  fixed 
imum. 


min- 


192.  Two-party  Time  Draft.  By  substituting  for  tlie  words 
"At  sight"  in  the  preceding  illustration,  such  words  as 

Ten  days  after  date, 
At  thirty  days'  sight,  or 
Thirty  days  after  sight 

the  draft  becomes  a  time  draft.  Instead  of  paying  this  draft  when 
it  is  first  presented,  Mr.  Osborne  will  accept  it ;  that  is,  he  will 
agree  to  pay  it  when  it  is  due.  Acceptance  consists  of  writing 
across  the  face  of  the  draft  the  word  "  Accepted"  and  signature. 

193-  Maturity  of  Time  Drafts.  Drafts  payable  "after  sight"  or 
"  at  —  days'  sight "  are  payable  a  stated  number  of  days  after  accept- 
ance, and  the  acceptance  should  therefore  be  dated.  Drafts  pay- 
able "after  date"  become  due  a  stated  number  of  days  after  the 
date  of  the  draft.  The  acceptance,  therefore,  does  not  need  to  be 
dated,  but  it  usually  is. 


^.  ^.^^.A- 


9B^J^  c^.^^.^^.,'.,  d^Ji 


Li^22=r- 


An  Accepted  Time  Draft 

This  draft  is  due  ten  days  after  June  5,  or  June  15. 

194.   Three -party  Drafts.       T.  D.    Morrison  of   Chicago  owes 
A.  J.  Sellers  of  New  York  $85.00. 

Mr.    Sellers  owes  G.   A.   Davis  &   Co.    of  Chicago   f$  150.00. 


COLLECTING  BILLS  .   231 

Mi\   Sellers  draws  the  following  draft,   asking  Mr.  Morrison  to 
pay  G.  A.  Davis  &  Co.  185.00. 


i 

t 

■ /£,^^^y/      ^^.  ^  "^^.y^^^^   '=^                           '^  ^' 

i 

/oL^.^!^^^^/"^^^ /'^ ^ — ~   ^V)y?^AA 

1 

'%-                        '^^^.-.^a-^  <:Z^^^                       /^ 

-     ^          ^       ■ 

Three-party  Sight  Draft 

Oral  Work 

What  two  parties  make  a  payment  when  this  draft  is  used? 

Explain  how  one  transfer  of  money  is  saved. 

How  much  will  Sellers  owe  G.  A.  Davis  &  Co,  after  they  have 
received  this  draft  ? 

Three-party  drafts  may  also  be  made  payable  after  a  stated  time 
by  using  the  terms  explained  on  page  230. 

Written  Work 

1.  On  July  13,  you  purchased  from  A.  B.  Butler  of  Minneap- 
olis, Minnesota,  an  invoice  of  goods  amounting  to  i  123. 60  ,  terms, 
sight  draft  in  10  days,  less  3  %.  On  July  20,  Mr.  Butler  drew 
a  sight  draft  on  you  for  the  net  amount  of  the  bill.  He  indorsed 
the  draft,  and  gave  it  to  the  Fourth  Street  Bank  of  Minneapolis 
for  collection.  The  Minneapolis  bank  indorsed  it  and  sent  it  to 
the  First  National  Bank  of  your  city.  The  draft  was  presented 
to  you  by  the  bank  on  the  23d  of  July. 

Write  the  draft  with  indorsements. 

If  the  First  National  Bank  charged  15  cents  for  collection,  how 
much  did  Mr.  Butler  receive  in  payment  of  the  draft  ? 

How  much  did  you  pay  to  the  bank  ? 


232  COLLECTING  BILLS 

2.  You  purchased  an  invoice  of  goods  from  Winthrop  and 
Monroe  of  Toledo,  Ohio.  Amount  of  invoice,  i  365.00.  It  was 
your  first  transaction  with  them  and  consequently  you  were  un- 
known to  them.  As  you  wanted  the  goods  immediately  and  did 
not  wish  to  delay  while  inquiries  were  made  regarding  your  credit, 
you  instructed  them  to  send  the  goods  by  freight  and  send  a  sight 
draft,  with  bill  of  lading  attached,  to  the  First  National  Bank  of 
your  city.  The  sight  draft,  which  was  dated  yesterday,  arrived 
this  morning.  It  was  made  payable  to  Winthrop  and  Monroe 
and  was  indorsed  to  the  order  of  the  bank. 

Write  the  draft  and  show  the  indorsement  made  by  Winthrop 
and  Monroe. 

Write  a  check  in  favor  of  the  bank  to  pay  the  draft. 
What  will  you  receive  in  exchange  for  the  check  ? 
How  will  Winthrop  and  Monroe  get  their  money  ? 

3.  On  September  3,  you  purchased  an  invoice  of  goods  from 
S.  L.  Norton  of  Springfield,  Illinois.  Terms,  thirty-day  draft 
from  date  of  sale,  less  1%.  Amount  of  invoice,  $75.00.  On 
September  5,  you  received  the  draft  in  the  mail ;  it  was  dated 
September  3,  and  was  payable  30  days  after  date.  You  immediately 
accepted  the  draft  and  returned  it  to  Mr.  Norton. 

Write  the  draft,  and  show  your  acceptance. 
When  will  you  be  expected  to  pay  the  draft  ? 

4.  You  owed  S.  D.  Briggs  of  Winona,  Minnesota,  175.00  ; 
Mr.  Briggs  owed  F.  R.  Tuttle  of  your  city,  $136.00.  On  June  19, 
Mr.  Briggs  drew  a  sight  draft  on  you  for  the  amount  of  your 
debt,  and  sent  it  to  Mr.  Tuttle  as  part  payment  of  his  debt.  Mr. 
Tuttle  presented  it  to  you.  You  gave  Mr.  Tuttle  cash  in  payment 
of  the  draft,  and  received  the  draft  as  a  receipt. 

Write  the  draft. 

How  much  did  Briggs  owe  Tuttle  after  the  draft  was  paid  ? 


CHAPTER   XX 

FOREIGN  MONEY  AND  EXCHANGE 

FoEEiGN  Money 

195.  The  trade  between  the  United  States  and  foreign  coun- 
tries necessitates  changing  money  values  of  the  United  States 
coinage  into  that  of  foreign  countries,  and  also  changing  values 
stated  in  the  coinage  of  foreign  countries  into  that  of  the  United 
States.  In  order  to  provide  a  standard  of  comparative  values, 
the  Director  of  the  United  States  Mint  at  frequent  intervals 
estimates  the  values  of  foreign  coins,  and  these  values  are 
proclaimed  by  the  secretary  of  the  treasury.  This  proc- 
lamation is  then  used  as  the  standard  in  computing  the  value 
of  foreign  merchandise  imported  into  this  country,  until  the  suc- 
ceeding proclamation  is  issued.  The  data  in  the  table  on  the  fol- 
lowing page  are  copied  from  a  recent  proclamation. 

196.  To  reduce  a  value  in  foreign  coinage  to  United  States 
money. 

Multiply  the  value  of  the  coin  in  United  States  money  hy  the 
number  of  the  coins. 

Example.     Change  2500  francs  to  dollars. 

Solution.  1  franc  =  $  .193. 

2500  X  $.193  =  1482.50. 

197.  To  reduce  a  value  in  United  States  money  to  foreign 
coinage. 

Divide  the  value  in  United  States  money  hy  the  value  of  the  foreign 
unit. 

233 


234 


FOREIGN   MONEY  AND  EXCHANGE 


Example.     Change  $86.85  to  francs. 

Solution.  1  franc  =$.193 

$86.85  ^  $  .193  =  450,  the  number  of  francs. 

Values  of  Foreign  Coins 


Value 

Country 

Legal  Standard 

Monetaby 
Unit 

IN  Terms 

OF   U.S. 

Money 

Remarks 

Argentine  Republic 

Gold   .... 

Peso  .     . 

$0.9647 

Currency:  depreciated  paper, 
convertible  at  44  per  cent  of 
face  value. 

Austria-Hungary   . 

Gold   .... 

Crown    . 

.203 

Belgium    .... 

Gold  and  silver 

Franc     . 

.193 

Member  of  Latin  Union  ;  gold 
is  the  actual  standard. 

Canada      .     .' .     . 

Gold   .... 

Dollar    . 

1.000 

France  

Gold  and  silver 

Franc     . 

.193 

German  Empire     . 

Gold   .... 

Mark      . 

.238 

Great  Britain     .     . 

Gold   .... 

Pound 
sterling 

4.8665 

Greece 

Gold  and  silver 

Drachma 

.193 

Member  of  Latin  Union ;  gold 

Italy 

Gold  and  silver 

Lira  .     . 

.193 

is  the  actual  standard. 

Japan    

Gold    .... 

Yen    .     . 

.498 

Mexico 

Gold    . 

Peso  .     . 

.498 

Netherlands  .     .     . 

Gold    . 

Florin     . 

.402 

Newfoundland  .     . 

Gold   . 

Dollar    . 

1.014 

Norway     .... 

Gold   . 

Crown    . 

.268 

Panama     .... 

Gold    . 

Balboa   . 

1.000 

Peru 

Gold   . 

Libra      . 

4.8665 

Philippine  Islands 

Gold   . 

Peso  .    . 

.500 

Roumania      .    .     . 

Gold   . 

Leu    .     . 

.193 

Russia 

Gold   . 

Ruble     . 

.515 

Sweden     .... 

Gold   . 

Crown    . 

.268 

Switzerland  .     .     . 

Gold   . 

Franc     . 

.193 

Turkey      .... 

Gold    . 

Piaster  . 

.044 

Uruguay    .... 

Gold   . 

Peso  .     . 

1.034 

Venezuela      .    .     . 

Gold   . 

Bolivar  . 

.193 

Written  Work 

1.  The  following  table  gives  tlie  value  of  the  United  States 
imports  from,  and  exports  to,  various  European  countries  in  a 
recent  year.  Imports  are  stated  in  the  coinage  of  the  nation 
from  which  they  came ;  use  the  preceding  table  of  values  and 
change  the  values  to  United  States  coinage.     Exports  are  stated 


FOREIGN  MONEY  AND  EXCHANGE 


235 


in  the  coinage  of  this  country ;   change  these  values  into  the  coin- 
age of  the  nation  to  which  they  were  shipped. 


Country 

Imports  from 

Exports  to 

Great  Britain 

Germany 

France 

56,085,622  pounds  sterling 
720,085,605  marks 
645,328,797  francs 
215,945,179  francs 

88,478,696  florins 
248,852,481  liras 
124,138,326  francs 

35,528,936  crowns 

30,789,992  crowns 

82,333,960  crowns 

40,110,530  rubles 
9,852,709  piasters 

19,810,186  drachmas 

$564,372,186 

306,959,021 

135,388,851 

51,387,618 

103,702,859 

65,261,268 

855,355 

9,451,011 

8,331,723 

22,388,930 

21,515,660 

2,597,239 

966,641 

Belgium 

Netherlands 

Italy 

Switzerland 

Sweden 

Norway 

Austria-Hungary 

Russia 

Turkey 

Greece 

Rule  a  'form  and  enter  these  statistics,  showing  the  value  of 
imports  in  dollars,  and  the  value  of  exports  in  terms  of  the  coin- 
age of  the  country  to  which  the  merchandise  was  exported. 

2.  Half  a  dozen  pairs  of  gloves  were  bought  in  England  for 
£  1  28.      What  was  the  cost  of  1  pair  in  United  States  money  ? 


Foreign  Exchange 

Most  of  the  methods  used  for  the  transfer  of  money  and  the 
collection  of  accounts  between  persons  in  the  same  country  are 
also  available  when  the  persons  live  in  different  countries. 

198.  Postal  Money  Orders.  Domestic  money  orders  were  dis- 
cussed on  page  221.  The  following  table  of  rates  shows  the  cost 
of  international  postal  money  orders : 

When  payable  in  Apia,  Austria,  Belgium,  Bolivia,  Cape  Colony,  Costa  Rica, 
Denmark,  Egypt,  Germany,  Great  Britain,  Honduras,  Hongkong,  Hungary, 
Italy,  Japan,  Liberia,  Luxemburg,  New  South  Wales,  New  Zealand,  Orange 
River  Colony,  Peru,  Portugal,  Queensland,  Russia,  Salvadoi',  South  Australia, 
Switzerland,  Tasmania,  the  Transvaal,  Uruguay,  and  Victoria. 


236 


FOREIGN  MONEY  AND  EXCHANGE 


For  Orders  from                            ] 

Fob  Orders  from 

$00.01  to  $2.50      .     . 

.     .    10  cents 

$30.01  to  $40.00     .     . 

.     .   45  cents 

2.51  to     5.00      .     . 

.     .15  cents 

40.01  to    50.00     .     . 

.     .    50  cents 

5.01  to     7.50      .     . 

.     .    20  cents 

50.01  to     60.00     .     . 

.     .    60  cents 

7.51  to  10.00      .     . 

.     .    25  cents 

60.01  to    70.00     .     . 

.     .    70  cents 

10.01  to  15.00      .     . 

.     .    30  cents 

70.01  to    80.00     .     . 

.     .    80  cents 

15.01  to  20.00      .     . 

.    35  cents 

80.01  to     90.00     .     . 

.     .    90  cents 

20.01  to  30.00      .     . 

.     .    40  cents 

90.01  to  100.00     .     . 

.     .    1  dollar 

When  payable  in  any 

ether  foreign  country. 

For  Oedbks  from 

For  Orders  from 

$00.01  to  $10.00    .     . 

.     .    10  cents 

$50.01  to  $60.00     .     . 

.     .    60  cents 

10.01  to     20.00    .     . 

.     .    20  cents 

60.01  to     70.00     .     . 

.     .   70  cents 

20.01  to     30.00    .     . 

.     .    30  cents 

70.01  to     80.00     .     . 

.     .    80  cents 

30.01  to     40.00    .     . 

.     .    40  cents 

80.01  to     90.00     .     . 

.     .    90  cents 

40.01  to     50.00    .     . 

.     .    50  cents 

90.01  to  100.00     .     . 

.     .    1  dollar 

199.  Bills  of  Exchange.  Bills  of  exchange  are  drafts  of  a  per- 
son or  a  bank  in  one  country  on  a  person  or  a  bank  in  another 
country.  They  are  of  three  kinds ;  Bankers'  Bills,  Commercial 
Bills,  and  Letters  of  Credit.  Formerly,  when  the  danger  of  long 
delays  and  possible  loss  in  the  foreign  mails  was  greater  than  it 
is  at  present,  foreign  bills  of  exchange  were  issued  in  sets  of 
three;  the  first  to  arrive  at  its  destination  was  paid  and  the 
others  became  worthless  automatically.  Later,  the  number  was 
reduced  to  two,  and  it  is  now  customary  for  only  one  of  the  set 
to  be  mailed,  and  the  other  filed  for  use  in  case  the  first  is  lost. 

200.  Bankers'  Bills.  A  banker's  bill  of  exchange  is  a  draft 
drawn  by  a  bank  in  one  country  on  a  bank  in  a  foreign  country. 
It  corresponds  to  the  bank  draft  of  domestic  exchange. 


FfAimis  TiuTST.vxipLSlvviNGS  Bank       ///,,^ 


C_D 


Paytotiik 

UIIDKK  «>£ 


^  IZK^rrisO'rustandSamngsBaxk 


CRCDIT   lYOriNAO 


^^-^^^^^ 


FOREIGN  MONEY  AND  EXCHANGE 


237 


Banker's  Bill 


201.  Commercial  Bills.  A  commercial  bill  of  exchange  is  a 
draft  drawn  by  a  shipper  of  merchandise  upon  a  foreign  buyer  or 
his  representative.  Commercial  bills  are  made  payable  either  at 
sight  or  after  a  certain  time.  If  such  a  bill  is  payable  in  less  than 
thirty  days,  it  is  known  as  a  short  hill;  if  in  thirty  days  or  more, 
it  is  known  as  a  long  MIL 

If  the  bill  is  accompanied  by  a  bill  of  lading  and  other  shipping 
papers,  it  is  known  as  a  documentary  hill;  if  no  papers  accompan}^ 
it,  it  is  known  as  a  clean  hill. 


^^^^^>5: 


(Tc 


/A_yML- 


Commercial  Bill 


238  FOREIGN  MONEY  AND  EXCHANGE 

A  documentary  hill  is  accompanied  by  the  bill  of  lading,  the 
invoice  of  the  goods,  and  usually  by  the  insurance  certificate. 

202.  Sending  Money  by  Banker's  Bill.  When  it  is  desired  to 
send  money  abroad,  a  banker's  bill  may  be  purchased  from  the 
bank  in  much  the  same  manner  that  a  domestic  bank  draft  is 
purchased.  In  fact,  bankers'  bills  are  frequently  called  foreign 
bank  drafts.  The  banker's  bill  is  sent  abroad  by  the  purchaser 
in  payment  of  his  debt. 

203.  Collecting  Accounts  by  Using  Commercial  Bills.  When  it 
is  desired  to  collect  an  account  from  a  foreign  debtor,  a  merchant 
may  draw  a  commercial  bill  and  leave  it  with  his  bank  for  collec- 
tion. The  method  of  collecting  the  bill  is  similar  to  that  em- 
ployed by  banks  in  the  collection  of  domestic  sight  or  time  drafts. 

204.  Securing  Immediate  Payment  for  Goods  by  Using  Documen- 
tary Bills.  Exporters  often  obtain  immediate  payment  for  goods 
sent  abroad  by  the  following  method.  The  goods  are  delivered 
to  the  transportation  company  and  a  bill  of  lading  is  received  by 
the  shipper.  The  goods  are  insured  against  loss  in  transit,  and 
a  certificate  of  insurance  is  received  from  the  insurance  company. 
The  shipper  draws  a  bill  of  exchange  on  the  foreign  importer, 
and  attaches  the  bill  of  lading  and  the  certificate  of  insurance  to 
the  bill  of  exchange,  thus  creating  a  documentary  bill.  The 
three  papers  are  indorsed  to  the  order  of  a  bank  which  purchases 
the  draft.  The  exporter  thus  receives  payment  for  his  goods  at 
the  time  of  shipment.  If  the  bill  cannot  be  collected,  the  goods 
are  taken  in  payment.  If  the  goods  are  lost,  the  certificate  of 
insurance  guarantees  that  the  bank  will  receive  payment  from 
the  insurance  company.  The  bank,  in  turn,  indorses  the  docu- 
ments and  sends  them  to  some  foreign  bank,  receiving  credit  for 
the  bill  of  exchange.  The  foreign  bank  collects  the  bill  from  the 
exporter. 

The  following  summary  illustrates  the  method  of  collecting  a 
documentary  bill  of  exchange  : 

American  Exporter   sells  the   documentary  bill  to  an  American 
Bank,  and  receives  cash. 


FOREIGN  MONEY  AND  EXCHANGE  239 

American  Bank  sends  the  documentary  bill  to  a  foreign  bank, 
and  receives  credit  against  which  it  can  draw  bankers'  bills. 

Foreign  Bank  collects  the  documentary  bill  from  the  foreign 
importer. 

205.  Rates  of  Exchange.  The  amount  which  a  bank  will  pay 
for  a  commercial  bill  and  the  amount  which  it  will  charge  for  a 
banker's  bill,  depend  upon  the  rate  of  exchange  existing  between 
the  countries  involved  in  the  transaction. 

The  mint  par  of  exchange,  as  shown  by  the  table  on  page  234,  is 
the  actual  value  of  the  coin  of  one  country  stated  in  terms  of  the 
coin  of  another  country.     It  remains  comparatively  constant. 

The  rate  of  exchange  is  the  market  value  of  a  bill  of  exchange. 
These  values  or  rates  of  exchange  are  constantly  fluctuating, 
because  the  value  of  a  bill  of  exchange,  like  the  value  of  other 
property,  varies  with  the  supply  and  demand. 

As  we  have  seen,  bankers  buy  documentary  bills  to  send  abroad 
to  create  a  deposit  against  which  they  can  draw  bankers'  bills. 
At  a  time  when  American  exporters  are  shipping  large  quantities 
of  goods  abroad,  documentary  bills  on  London  will  be  plentiful. 
American  bankers  can  easily  procure  all  of  these  bills  they  desire 
in  order  to  keep  up  their  balance  in  foreign  banks.  Supply  will 
be  relatively  much  greater  than  demand,  and  the  price  will  there- 
fore be  low.  Exchange  on  England  will  be  below  par,  or  at  a 
discount. 

Par  is  f  4.8665.  If  the  rate  of  exchange  is  below  par,  gay  at 
$4.84,  the  man  who  sells  a  documentary  bill  on  London  may  re- 
ceive for  it  less  than  its  face ;  while  the  man  who  wishes  to  buy 
a  banker's  bill  payable  in  London  may  buy  it  for  less  than  its  face. 

On  the  other  hand,  let  us  assume  a  condition  when  American 
imports  greatly  exceed  exports.  While  imports  are  being  made 
in  large  quantities,  American  banks  will  have  frequent  demands 
for  bankers'  bills  to  send  abroad  in  payment  for  goods.  In 
order  to  issue  these  bills,  American  banks  must  maintain  a  large 
deposit  in  the  foreign  banks.  To  keep  up  this  large  balance,  they 
will  require  numerous  documentary  bills  payable  in  London.  But 
since  exports  are  low,  the  supply  of  these  documentary  bills  will 


240  FOREIGN  MONEY  AND  EXCHANGE 

be  small,  and  bankers  will  bid  against  each  other  to  obtain  them. 
This  will  cause  the  rate  of  exchange  to  go  above  par.  This  means 
that  the  American  exporter  can  obtain  more  than  $4.8665  per 
pound  sterling  for  documentary  bills  on  London  which  he  has  for 
sale ;  while  the  importer  who  wishes  to  send  money  abroad  will 
have  to  pay  more  than  $4.8665  per  pound  sterling  for  bankers'  bills. 

206.  Quotations  of  Rates  of  Exchange.  Exchange  on  Great 
Britain  is  quoted  at  the  number  of  dollars  to  the  pound  sterling. 
4.87  means  that  a  pound  bill  on  London  will  cost  $4.87. 

Exchange  on  the  Latin  Countries  (France,  Spain,  Switzerland, 
and  Italy)  is  quoted  at  the  number  of  foreign  coins  per  dollar. 
Exchange  on  France,  quoted  at  5.15|^,  means  that  5.15|^  francs 
can  be  purchased  for  il.OO. 

.  Exchange  on  Germany  is  quoted  at  the  number  of  cents  per 
four  marks.  95  means  a  banker's  bill  for  four  marks  can  be  pur- 
chased for  95  cents. 

Many  banks  receive  daily  the  quotations  of  foreign  exchange. 

The  following  is  an  extract  from  such  a  quotation : 

London  Cables  4.8915 

London  Demand  4.8865 

Sixty  Day  Grain  4.8625 

Paris  Checks  5.15 

Berlin  95f 

To  find  the  cost  of  a  banker's  bill  on  London. 

Example.  What  is  the  cost  of  a  £600  draft  on  London,  pur- 
chased at  4.8675? 

Solution.  $  4.8675      Cost  per  pound 

^600  Number  of  pounds 

$  2920.50      Cost  of  £  600  draft 

To  find  the  cost  of  a  draft  on  Paris. 

Example.  What  is  the  cost  of  a  300-franc  draft  on  Paris,  pur- 
chased at  5.15? 

Solution.     5.15  francs  cost  $  1.00. 

300  francs  will  cost  as  many  dollars  as  5.15  is  contained  in  300;  therefore 
the  cost  is  ^58.25. 


FOREIGN  MONEY  AND  EXCHANGE 
To  find  the  cost  of  a  draft  on  Berlin. 


241 


Example.  What  is  the  cost  of  a  1000-mark  draft  purchased 
at  951? 

Solution.    1000  -r-  4  =  250,  number  of  lots  of  4  marks  purchased. 
^.95i  X  250  =  ^238.13. 

Reverse  these  processes  to  find  the  value  in  foreign  coinage 
of  drafts  purchasable  with  a  specified  amount  of  United  States 
money. 

207.  Travelers'  Checks.  Travelers'  checks  are  issued  by  the 
express  companies  and  by  the  American  Bankers  Association. 
These  checks  are  issued  in  denominations  of  United  States  money, 


but  show  on  their  face  their  cashable  value  in  the  coinage  of 
foreign  countries.  The  purchaser  signs  the  checks  when  pur- 
chased, and  again  when  cashed,  as  a  means  of  identification.  The 
cost  of  the  checks  is  the  face  plus  ^  %  commission. 

208.  Letters  of  Credit.  A  letter  of  credit  is  a  circular  letter 
addressed  to  the  correspondents  of  the  issuing  bank,  introducing 
the  holder,  certifying  that  he  is  authorized  to  draw  a  certain  sum 
of  money,  and  requesting  that  his  drafts  be  honored  up  to  that 
amount.  By  depositing  cash  or  securities  with  a  bank,  a  traveler 
can  obtain  a  letter  of  credit.  This  document  is  drawn  by  the  bank 
in  which  the  cash  has  been  deposited.  When  a  bank  issues  a 
letter  of  credit,  it  thereby  authorizes  its  correspondents  (banks  in 


242 


FOREIGN  MONEY  AND  EXCHANGE 


which  it  has  money  on  deposit)  to  pay  drafts  drawn  by  the 
traveler  up  to  a  specified  sura.  The  bank  also  furnishes  the  pur- 
chaser a  Letter  of  Indication  containing  his  signature ;  when  the 

(Eirrulm*  JPrltrr  uf  (Hxtbxt. 


c^.OOOO 


Harris  Trust  and  Samngs  Bank 

ORGANIZED  AS  ^.W:HAIUaS  &  CO.,1882.  INCORPORATED  1907. 


(Qj^/i^T/un^ 


'^am/t^^i 


^ 


/^ha^ 


traveler  presents  a  draft  to  one  of  the  foreign  banks  specified  in 
the  letter  of  credit,  the  signature  on  the  draft  is  compared  with 
that  on  the  letter  of  indication.     If  the  signatures  are  identical^ 


FOREIGN  MONEY  AND  EXCHANGE 


243 


OBLIGATION. 
FOREIGN  LETTER  OF  CREDIT. 


fonn4S-B.    tu:07. 


VAT  ^    / 


^5 


It 


/^ 


ungrantinsto L'ZZZTL^ a  circular  LETTER 


Chicago 

HARRIS  TRUST  AND  SAVINGS  BANK.^>^ 

'Dear  Sirs:  In  consideration  of ydurjjsrantinr  *"    ' '^'^ 
OF  CREDIT  onJ^:^S:::±^ 

No Q..^.. ...Jn  fayorffL^^Lh.......y ..^„^^ — ..■ ^ .. 

for. ^^.:^.09,,Z.,..:^^^ 

of  which Ciiik-.... acknowledge  redeipt, ^..._ hereby  engage  to  pay  on  presentation,^ 

in  United  States  Currency  {at  the  current  ratSaf  exdmnge),  any  and  all  sums  that  may 
from  time  to  time  be  drawn  under  said  Letjer  of  Credit,  and  also  a  commission  of  one  per 

cent;  or .?r-fL ........authorize  you  todklrgetkesame  to    /i^-<^ account  with  you. 

As  coltnteral  security  for  the  prompt  faymepif  at  maturity  of  any  oj/tbe  obligations  contemplated 
above S>i...... 


^have  deposited  with 


^^CDOO 


vtng  described  properly  : 


W^^.^Js...^- 


which  youy  or  your  asVipns,  ^It  hereby  authorized  to  sell  in  whole  or  in  part  upon  the  non- performance 
of  this  promise  or  the  nffta^aymen/at  maturity  of  any  of  the  obligations  contemplated  above,  or  at  any 
time  or  times  thereafter  jGJ  puNu  or  private  sale,  without  advertising  the  same  or  demanding  payment, 
or  giving  notice,  and  to\npl/i^uch  of  the  proceeds  thereof  to  the  payment  of  such  indebtedness  as  may 
be  necessary  to  pay  the  same  with  all  interest  due  thereon,  and  also  to  the  payment  of  all  expenses 
attending  the  sale  of  said  property,  returning  the  over- plus  to  the  underisgned,  who  shall  remain  liable 
for  the  prompt  payment  of  any  deficiency  or  deficiencies  arising  on  account  of  such  sale. 

Yours  tr 


the  foreign  bank  pays  the  draft,  charges 
the  amount  to  the  bank  issuing  the 
letter,  and  indorses  the  amount  of  the 
draft  on  the  letter.  Thus,  the  letter 
of  credit  shows  at  all  times  the  balance 
remaining  subject  to  draft.  When  a 
draft  is  drawn  which  exhausts  the 
balance,  the  letter  is  surrendered,  and 
sent,  together  with  the  draft,  to  the 
issuing  bank. 

Letters  of  credit  are  issued  in  an 
amount  equivalent  to  the  exchange 
value  of  the  cash  or  securities  deposited, 
minus  a  percentage  charged  for  the  ac- 
commodation. 


HARRIS  TRUST  AND  SAVINGS    BANK 


INCORPORATCO   1607 

Chicago,  u.  s.  a. 

To  Messieurs  The  Kinks 

and  Bankers  hiamed  Herein: 

The  Bearer  of  this  Letter, 


«5  been  supplied  with  our  Circular 
*     Letter  of  Credit  No.   OO 
HARRIS  TRUST  AND  SAVINGS   BANK 


244  FOREIGN  MONEY  AND  EXCHANGE 

Written  Work 

1.  Find  the  total  cost  of  a  postal  money  order  for  |585,  payable 
in  Hongkong. 

2.  Find  the  total  cost  of  a  postal  money  order  for  $  215.65,  pay- 
able in  Paris. 

3.  What  would  be  the  cost  of  a  London  draft  for  £  115,  ex- 
change  being  quoted  at  4.8675  ? 

4.  A  man  had  f  500  which  he  wished  to  remit  to  his  mother  in 
Paris.  How  many  francs  did  she  receive,  the  rate  of  exchange 
being  5.15? 

5.  A  man  residing  in  this  country  wished  to  send  his  nephew 
in  Berlin  a  birthday  present  of  $10.  What  was  the  amount  of  the 
draft  in  marks,  exchange  being  at  95 J  ? 

6.  M.  Le  Count,  traveling  in  America,  presented  to  a  Chicago 
bank  a  draft  on  the  Credit  Lyonnais,  Paris,  for  2000  francs.  How 
much  American  money  did  he  receive,  exchange  being  quoted  at 
5.16? 

7.  The  Western  Milling  Co.  sold  a  Glasgow  customer  three 
hundred  barrels  of  XXXX  flour  at  19s.  per  barrel.  The  Milling 
Co.  sold  its  sixty-day  time  bill,  with  bill  of  lading  attached,  to 
its  banker  for  4.86|-  per  pound  sterling.  What  was  the  amount 
of  the  draft  in  English  currency,  and  how  much  per  barrel  United 
States  currency  did  the  company  receive  for  its  flour  ? 

8.  The  Lincoln  Grain  Co.  sold  three  cars  of  wheat  to  a  Liver- 
pool miller  at  4s.  per  bushel.  The  net  weight  of  the  cars  was : 
58,950#,  59,040#,  and  64,360#.  The  bank,  as  agent  for  the 
grain  company,  sold  the  draft  with  bill  of  lading  attached  at 
4.8555.      How  much  did  the  Grain  Company  receive  ? 


CHAPTER   XXI 


ACCOUNTS 


An  account  is  an  orderly  record  of  the  transactions  pertaining 
to  any  one  person  or  thing. 

209.    The  Cash  Account.     In  keeping  a  record  of  cash, 

All  cash  receipts  are  entered  on  the  left,  or  debit  side ; 

All  cash  payments  are  entered  on  the  right,  or  credit  side ; 

The  difference  between  the  total  receipts  and  total  payments  is 
the  balance  of  cash  on  hand. 

The  following  transactions  are  recorded  in  the  model  cash  ac- 
count in  the  illustration. 

April  6, 1915,  C.  D.  Smith  invested  15000  in  business;  April  7, 
he  paid  $1640  for  goods;  April  9,  he  paid  his  store  rent,  $75; 
April  10,  he  received  $275  for  merchandise ;  April  13,  he  received 
$36  from  John  Appleton;  April  14,  he  paid  F.  G.  Barton  $128; 
April  16,  William  Hobart  paid  him  $60  on  accoujit ;  April  28, 
he  paid  D.  F.  Hilton  $30  on  account. 


K^^.^^ 

^^ 

^ 

^^^^.:^. 

^CC 

\^111/ 

■^ 

■^^^yS^^'A^A^^ 

/6^ 

' 

/r> 

^g^^.^3^^. 

2a 

s  — 

/27 

a^^.,^a>.y- 

/■>, 

(L-A^^^^A/b,^ 

<^ 

/iJ. 

/2 

^ 

^yy.^^B^:^^. 

^ 

^ j 

^/? 

s^^^^C'j^.. 

3 

-^n 

^^.Z.,,z^^ 

_i26fc 

i? 

<5i2 

. . 

^2-? 

1/- 

^^«^ 

/ 

^^y^^j-^. 

^£2 

5 

^ 

y 

210.  Personal  Accounts.  Transactions  with  persons  are  re- 
corded in  personal  accounts.  Persons  to  whom  goods  are  sold 
are  debited  for  all  goods  sold  to  them  on  account;  they  are 
credited  for  payments  made  by  them  on  account. 

245 


246 


ACCOUNTS 


Persons  from  whom  goods  are  bought,  are  credited  for  goods 
purchased  from  them  on  account ;  they  are  debited  for  payments 
made. to  them  on  account. 

The  two  illustrations  which  follow  will  show  the  two  common 
rulings  for  personal  accounts. 

May  1,  1915,  purchased  from  Harold  Booth,  merchandise,  -f  260. 

May  7,  purchased  merchandise  from  him,  $37.90;  May  10, 
paid  him  for  the  invoice  of  May  1,  less  1  %  discount.  Cash  #257.40, 
Discount  $2.60;  May  17,  paid  him  for  the  invoice  of  May  7, 
less  1%  discount,  Cash  $36.52,  Discount  $.38;  May  20,  pur- 
chased merchandise,  $271.25. 


.%;>,.^.^^u^ 


/f/^ 


%^^^  AS-y 


2.i,o 


&£o 


M^ 


^^.^-^ 


£^£ 


7^^ 


^^<^-^ 


^^rZ^- 


2^£. 


June  1,  1915,  sold  to  B.  A.  Newcomber,  goods  amounting  to 
$345.70;  June  4,  sold  to  Newcomber  merchandise  amounting  to 
$38.45  ;  June  11,  received  payment  for  invoice  of  June  1,  less  2%, 
Cash  $338.79,  Discount  $6.91;  June  12,  sold  Newcomber  an  in- 
voice amounting  to  $83.92;  June  14,  received  payment  for  the 
invoice  of  the  4th,  less  1%,  Cash  $38.07,  Discount  $.38. 


(^  C^,    yZc^:<^-c^^^^.^/^yt^ 


Date 


Sale 


Cash 


Discount 


Balance 


3AC^ 


n 


^¥^ 


^ 


/^ 


Z^ 


J^^ 


.A^ 


6L5. 


^ 


^.3^5 


.^3. 


7^ 


^ 


^s_ 


A5. 


ACCOUNTS  247 

211.  Accounts  Receivable  and  Accounts  Payable.  If  a  person's 
account  is  larger  on  the  debit  side,  it  shows  a  balance  owed  hy 
that  person ;  it  is  .therefore  an  account  receivable,  and  the  balance 
is  a  resource. 

If  a  person's  account  is  larger  on  the  credit  side,  it  shows  a 
balance  owed  to  that  person ;  it  is  therefore  an  account  payable, 
and  the  balance  is  a  liability. 


Written  Work 

1.  Rule  a  cash  account  and  enter  the  following  transactions ; 
find  the  balance,  and  rule  the  account. 

August  2,  you  invest  15000  in  a  grocery  business;  August  B, 
purchase  merchandise,  paying  cash  for  the  same,  $1345.75 ; 
August  6,  receive  cash  for  merchandise  sold,  $127.50  ;  August  10, 
receive  cash  for  goods  sold,  §50.25  ;  August  12,  pay  for  advertis- 
ing, $5.60  ;  August  17,  receive  cash  for  merchandise  sold,  $23.74  ; 
August  18,  pay  cash  for  an  invoice 'of  merchandise,  $56.35; 
August  21,  receive  cash  from  Henry  Belmont  on  account, 
$45.80  ;  August  23,  pay  cash  to  Oscar  Haines  on  account,  $54.85 ; 
August  31,  pay  store  rent,  $30,  and  clerk  hire,  $35. 

2.  Rule  a  personal  account  similar  to  the  illustration  of  Harold 
Booth's  account,  page  246,  and  enter  the  following  transactions : 

September  3,  you  purchase  from  R.  G.  Henderson,  on  ac- 
count, 2/10;  N/60,  an  invoice  of  goods  amounting  to  $237.40; 
September  9,  purchase  an  invoice  of  goods  from  Henderson, 
$58.35,  terms  1/15;  N/2  months;  September  11,  purchase  an 
invoice  of  merchandise  from  Henderson,  $123.60,  terras  2/5; 
N/30 ;  September  12,  pay  the  invoice  of  the  3d,  less  the  dis- 
count;  September  14,  purchase  goods  amounting  to  $25;  Sep- 
tember 16,  pay  the  invoice  of  the  11th,  less  the  discount.  What 
is  the  balance  of  Mr.  Henderson's  account  ?  Is  this  an  account 
receivable  or  an  account  payable  ?  Is  the  balance  a  resource  or 
a  liability  ? 

3.  Rule  an  account  similar  to  the  illustration  of  B.  A.  New- 
comber's  account,  page  246,  and  enter  the  following  transactions  ; 


248  ACCOUNTS 

July  2,  sold  R.  S.  Clark,  terms  1/5;  N/30,  merchandise  amount- 
ing to  $57.82;  July  5,  sold  Clark  goods  to  the  value  of  123.95, 
terms  2/10 ;  N/60  ;  July  7,  received  payment  for  the  invoice  of 
the  2d,  less  the  discount;  July  9,  sold  Clark  an  invoice  of  $75, 
less  a  trade  discount  of  10%,  terms  1/10;  N/30;  July  11,  sold 
him  a  bill  of  goods  amounting  to  $40 ;  July  15,  received  cash  for 
the  invoice  of  the  5th,  less  the  discount. 

Is  this  account  an  account  receivable  or  an  account  payable  ? 

Is  the  balance  a  resource  or  a  liability? 


CHAPTER   XXII 


TAKING   INVENTORY 


At  certain  regular  intervals  an  inventory  is  taken  to  determine 
the  value  of  the  stock  on  hand.  Two  clerks  usually  work  to- 
gether in  taking  the  inventory.  One  counts  the  number  of  items 
of  each  kind,  and  reads  aloud  the  cost  price  marked  on  the  goods. 
The  second  clerk  records  these  facts.  The  inventory  is  then  sent 
to  the  oflQce,  where  the  value  of  each  item  is  extended  and  the 
total  value  of  the  stock  on  hand  is  determined. 

Inventories  are  entered  in  various  forms,  depending  upon  the 
details  of  information  desired. 


212.    Periodic  Inventories, 
may  be  used : 


A  simple  form   like  the  following 


QVAIfTITY 

NAME  on  T£M 

COST 

COST 
rXTEAS/OU 

/^Ul. 

^.^.t^t/^  C^^lC^^^yt. 

S 

Co 

/  oC 

¥0 

34'^ff' 

/— ^&^^ 

^6 

2^ 

JO 

&8]^^ 

^^&'^/&-ft^  C^^^^ 

¥^ 

/:2 

zt^ 

Written  Work 

Rule  an  inventory  similar  to  the  preceding  form,  enter  the  fol- 
lowing items,  find  the  cost  of  each  item,  and  the  total  cost. 

This  is  one  of  several  inventory  sheets  used  in  taking  stock  in 
a  grocery. 


87 

lb. 

Mexican  Java  Coffee 

lb. 

%   .23- 

136 

lb. 

Ceylon  Tea 

lb. 

.42 

167 

Pkg. 

Half-pounds  Ceylon  Tea 

lb. 

.47 

2 

cases 

Boneless  Herring  (4  doz.) 
249 

doz. 

1.10 

250 


TAKING  INVENTORY 


Salt  Mackerel 

Cans  Corn 

Cans  Tomatoes 

Cans  Peas 

Cans  Beans  . 

Bottles  Olives 

Bottles  Olives  (18  oz.) 
doz.   Bottles  Stuffed  Olives  (10  oz.) 

Evaporated  Apricots 

Evaporated  Apples 

Dried  Prunes 

Dried  Peaches 

Seedless  Raisins 
case  Currants  (36  lb.) 


A  more  elaborate  form  of   inventory  similar  to  the  following 
may  be  used  when  desired. 


83 

lb. 

8f 

doz. 
doz. 
doz. 

H 

doz. 

H 

doz. 

H 

doz. 

345 

doz. 
lb. 

163 

lb. 

109 

lb. 

230 

lb. 

67 

lb. 

1 

case 

lb. 

$   .22 

doz. 

.85 

doz. 

.95 

doz. 

1.25 

doz. 

1.35 

doz. 

1.00 

doz. 

3.20 

doz. 
lb. 
lb. 
lb. 
lb. 

.821 
.08} 
.07i 
.05J 
.07| 

lb. 
lb. 

.09i 
.08J 

Add 

Deduct 

Lot  No. 

Size 

Name  and  Quantity 

Cost 
Price 

Cost 
Extension 

% 
Dep. 

Loss 
As- 
turned 

c4  M^ 

6 

3  S2*«^^*«^  ^*«.%«^&^  O^.^^^ 

£ 

so 

S 

¥c 

/ 

■:^  t/^^ 

d'A 

^^2*^^    ,*^ 

C 

8o 

g 

^0 

¥ 

c/  vs. 

7 

^9PaU^    ,.<si- 

a 

So 

zs 

20 

s/-^^ 

7'/- 

^5:^.^  .<{^ 

z 

So 

/& 

sc 

c/  ^£ 

s 

S.'^^<A^    U<^ 

£ 

So 

^ 

4o 

«5. 

i-fc 

3  ^S^  ^^?:*^  a^iLc/^^  (S^ii^^.^ 

3 

/o 

9 

30 

/oYo 

.f3 

213.  Explanation  of  Form.  The  Lot  Number  is  a  number  given 
an  article  by  either  the  manufacturer  or  the  merchant.  Since 
different  styles  of  goods  are  given  different  lot  numbers,  this  num- 
ber may  be  entered  in  the  inventory  in  place  of  a  description. 


TAKING  INVENTORY  251 

The  "  size  "  column  is  used  to  show  the  different  sizes  of  an  article 
in  stock.  As  illustrated  in  the  model  inventory,  each  size  of  an 
article  may  appear  on  a  separate  line,  or  all  sizes  may  be  entered 
on  the  same  line.  When  the  latter  method  is  followed,  the  quan- 
tity of  a  certain  size  is  indicated  by  writing  the  size  below  a  short 
line,  and  the  number  of  articles  of  that  size  above  the  line.     Thus, 

|,  ^,  means  3  No.  7's,  5  No.  8's. 
7    8 

When  an  error  is  made  in  the  count,  this  error  may  be  corrected 
by  using  the  "  Add  "  or  "  Deduct "  columns.  "  These  columns  are 
also  used  when  goods  are  purchased  or  sold  while  the  inventory 
is  being  taken.  By  adding  goods  purchased,  and  deducting  goods 
sold  during  the  taking  of  inventory,  the  value  of  stock  at  the  end 
of  the  inventory  may  be  determined. 

To  find  the  cost  extension,  multiply  the  cost  by  the  number  of 
items  plus  the  number  of  items  in  the  "  Add  "  column  or  minus 
those  in  the  "  Deduct  "  column. 

If  goods  become  shopworn  or  out  of  style,  if  the  market  price 
has  decreased,  or  if,  for  any  other  reason,  the  value  has  become  less 
than  the  cost  marked  on  the  goods  and  entered  in  the  inventory, 
it  is  necessary  to  make  some  allowance  for  this  depreciation  in 
value. 

Perhaps  an  article  is  worth  only  half  its  cost  price.  In  that 
case  a  50  %  depreciation  should  be  entered  in  the  "  %  Deprecia- 
tion "  column.  Then  50  %  of  the  cost  extension  for  that  item  is 
entered  in  the  "  Loss  Assumed "  column,  and  the  total  of  this 
column  is  subtracted  from  the  total  of  the  "  Cost  Extension " 
column  to  determine  the  actual  value  of  the  stock  on  hand. 

Oral  Work 

1.  What  does  25%  depreciation  mean?  10%  depreciation? 
20  %  depreciation  ? 

2.  If  stock  is  damaged  so  that  it  is  worth  only  |  of  its  original 
cost,  what  per  cent  depreciation  should  be  entered? 

3.  Goods  are  worth  |  of  their  original  cost.  What  is  the  per 
cent  depreciation? 


252  TAKING  INVENTORY 

4.  Goods  are  worth  ^  of  their  original  cost.  What  is  the  per 
cent  depreciation? 

5.  Goods  are  worth  J  of  their  original  cost.  What  is  the  per 
cent  depreciation? 

6.  An  article  purchased  for  f  3.20  can  now  be  bought  for  $2.80. 
What  per  cent  depreciation  should  be  entered  in  the  "per  cent 
depreciation"  column? 

7.  What  would  be  the  amount  of  the  loss  assumed  on  27  of 
the  articles  mentioned  in  problem  6  ? 

Written  Work 

Rule  an  inventory  form  similar  to  the  one  on  page  250  and  enter 
the  following  items  which  form  a  portion  of  the  inventory  of  a 
shoe  stock.  Enter  one  size  to  a  line,  find  the  value  of  each  item 
listed,  and  the  total  value  of  the  stock  shown  on  the  page  after 
making  corrections  for  stock  returned,  for  sales,  and  for  de- 
preciation. 

Lot  No.   219  B;?     i-,    ?,    A,    f      2.     Men's  Tan    Oxfords, 

6      6|-     7      7J     8     8^ 

$  3.15  per  pair. 
Lot   No.    712;    I    A,    4,    ^,    3,    ^,    2       Men's    Vioi    Kid 

Bluchers,  $2.90  per  pair. 

Lot  No.  322  A  ;   -,  ^,  -.     Romeos  at  11.90  per  pair. 
6    6^    7 

Lot  No.  618  Dl;    |,   A,   |,    2,   p,  1..      Men's    Russian    Calf 

7     7^     8     8^     9     9^ 

Boots,  8  3.20  per  pair. 
One  pair  of  Lot  No.  712,  Size  7,  taken  home  by  a  customer  be- 
fore taking  inventory,  was  returned  after  Lot  No.  712  was  listed. 
During  stock  taking,  the  following  sales  were  made ; 
1  pair  Lot  No.  712,  size  7J. 
1  pair  Lot  No.  618  Dl,  size  7^. 
1  pair  Lot  No.  618  Dl,  size  9^. 
Lot  No.  322  A  can  now  be  purchased  for  $1.75. 

214.  Perpetual  Inventory.  In  some  lines  of  business  a  perpetual 
inventory  is  kept.     It  is  also  called  a  Stock  Record.     When  such 


TAKING  INVENTORY 


253 


a  record  is  kept,  a  book  is  required  for  the  purpose,  one  page  being 
devoted  to  each  item  carried  in  stock.  Both  purchases  and  sales 
are  recorded  at  cost  price.  The  following  model  illustrates  a  form 
of  perpetual  inventory. 


9lcr   ^60^     (^ 


^Z^eSZx^S^f-- 


Danger  Point  /^ 


Date 


Purchases 


Sales 


Balance 


/<j/^ 


c^. 


No. 


<,o 


So 


Cost 


/S 


/S 


Yah 


No. 


/c  80 


^o 


£^6 


S.S 


Value 


No. 


n^a. 


60 

Ho 


Value 


S 
/8 


SO 

00 


254  TAKING  INVENTORY 

215.  Value  of  Perpetual  Inventory.  Considerable  labor  is  re- 
quired to  maintain  a  perpetual  inventory,  but  it  is  valuable  for 
several  reasons. 

When  stock  is  kept  in  warehouses  or  in  storerooms  at  some 
distance  from  the  salesrooms,  the  perpetual  inventory  is  a  great 
convenience  since  it  shows  without  delay  the  amount  of  stock  on 
hand. 

A  "  danger  point "  is  fixed  for  each  item.  When  the  balance 
on  hand  has  decreased  to  this  danger  point,  a  new  supply  is  pur- 
chased. 

An  inventory  may  be  taken  at  periodical  intervals,  and  the 
quantities  shown  compared  with  the  stock  record.  If  the  inventory 
and  the  stock  record  do  not  agree,  an  investigation  may  be  made 
to  discover  the  cause  of  the  discrepancy. 

Written  Work 

Rule  a  page  of  a  stock  record  similar  to  the  model  on  page  253, 
and  enter  the  following  facts,  making  a  perpetual  inventory  of  the 
stock  of  Solvay  Coke. 

Purchases 

October  22,  54,200#  at  $4.45  per  ton 

November  18,  57,600#         at  14.45  per  ton 
December  7,  52,800#  at  14.45  per  ton 

Sales 

October  29,  2  tons;  October  30,  5  tons;  October  31,  7500#; 
November  2,  9500#;  November  5,  7  tons;  November  17,  2  tons; 
November  19,  12  tons;  November  20,  7000 #;  November  23,  4 
tons;  November  24,  9000 #;  November  30,  2  tons;  December  9, 
13,000#;  December  11,  5  tons. 


CHAPTER   XXIII 
GROSS   TRADING   PROFIT 

216.  Definitions.  Gross  Trading  Profit  is  the  difference  between 
the  selling  price  and  the  cost  price. 

Net  Profit  is  found  by  subtracting  the  expenses  and  losses  of  the 
business  from  the  gross  profit. 

217.  The  Per  Cent  of  Gross  Trading  Profit  is  found  by  dividing 
the  gross  profit  by  the  net  sales. 

If  goods  are  sold  at  less  than  their  cost,  a  loss  results.  The 
per  cent  of  loss  is  found  by  dividing  the  loss  by  the  net  sales. 

Oral  Work 

1.  A  hat  which  cost  $  2  is  sold  for  1 3.  What  is  the  profit? 
What  is  the  per  cent  of  profit? 

2.  ^  A  set  of  books  cost  a  dealer  -120.  In  order  to  sell  them  the 
dealer  lost  f  2.00.     What  was  the  per  cent  of  loss? 

3.  Through  an  error  in  an  advertisement  a  merchant  was  obliged 
to  sell  some  parasols  at  16|%  less  than  their  cost.  He  lost  30 
cents  on  each  parasol.  What  did  they  cost,  and  what  was  the 
selling  price  ?  At  what  price  should  they  have  been  sold  to  gain 
10%  of  the  cost? 

Written  Work 

1.  Mr.  Fisher  bought  a  carriage  for  §55  and  sold  it  for  $75. 
What  was  the  gross  profit?  What  was  the  per  cent  of  gross 
profit  ? 

2.  During  a  certain  year  a  merchant  purchased  goods  which 
cost  him  il4,000.  At  the  close  of  the  year  this  stock  inventoried 
83000.     What  was  the  cost  of  the  goods  sold  ? 

His  sales  for  the  year  were  $14,080.  What  was  his  gross 
profit?     What  was  the  per  cent  of  gross  profit? 

255 


256 


GROSS  TRADING  PROFIT 


3.  The  inventory  of  a  dry  goods  merchant's  stock  at  the  begin* 
ning  of  the  year  was  $3560.  The  purchases  during  the  year  were 
f  28,265.  At  the  close  of  the  year  the  inventory  showed  a  stock 
of  f  3940  unsold.     What  was  the  cost  of  the  goods  sold  ? 

His  sales  for  the  year  were  $  31,673.  What  was  the  gross  profit? 
What  was  the  per  cent  of  gross  profit? 

218.  Buying  Expenses.  In  computing  the  cost  of  goods  pur- 
chased, it  is  customary  to  add  to  the  wholesale  price,  the  freight, 
drayage,  and  all  other  expenses  incurred  in  getting  the  goods  on 
the  shelves  ready  to  sell.  These  expenses  are  called  buying  ex- 
penses. 

Written  Work 

1.  Mr.  Tracey  bought  the  lumber  business  formerly  conducted 
by  Mr.  Boyce.  The  stock  on  hand  inventoried  15280.  Mr. 
Tracey's  purchases  during  the  year  were  $16,385.  The  freight 
was  $236,  the  cost  of  labor  in  placing  lumber  in  the  yards  and  all 
other  buying  expenses  $385.  At  the  end  of  the  year  the  stock 
inventoried  $6125.  What  was  the  cost  of  the  goods  sold  during 
the  year? 

If  the  sales  during  the  year  were  $  19,245,  what  was  the  gross 
profit  and  per  cent  of  gross  profit?         .  * 

2.  Complete  the  following  table  : 


Inven- 
tory, 

Jan.  1, 
19- 

Pur- 
chases 

Buying 
Expenses 

Total 
Cost  of 
Pur- 
chases 

Inven- 
tory, 
Dec.  31, 
19- 

Cost  of 
Goods 
Sold 

Sales 

Profit 

or  Loss 

Per 

Cent 

Profit 

OR  Loss 

8125 

75 

16,294 

90 

870 

25 

4685 

60 

18,495 

40 

5428 

80 

23,926 

56 

627 

90 

5626 

35 

88,756 

20 

1290 

00 

6,754 

00 

271 

25 

2140 

00 

8,325 

75 

4728 

50 

12,398 

80 

1417 

25 

1265 

70 

13,215 

75 

8680 

00 

15,927 

00 

485 

00 

2726 

00 

14,850 

00 

Enter  profit  and  per  cent  of  profit  in  black  ink. 
Enter  loss  and  per  cent  of  loss  in  red  ink. 


BORROWING   AND  LOANING 

CHAPTER   XXIV 

INTEREST 

If  you  should  rent  a  house,  you  would  agree  to  pay  a  certain 
sum  for  the  use  of  the  house  and  you  would  probably  sign  an 
agreement  to  pay  this  rent.  If  you  should  borrow  a  sum  of  money, 
you  would  probably  agree  to  pay  the  lender  a  certain  sum  for  the 
use  of  the  money  and  you  would  probably  be  required  to  sign  an 
agreement  to  repay  with  interest  the  sum  borrowed. 

219.  Terms  Used.  Money  paid  for  the  use  of  money  is  called 
interest.  Interest  is  usually  computed  as  a  certain  per  cent  of  the 
amount  borrowed.  The  per  cent  of  interest  is  called  the  rate  and 
the  amount  borrowed  the  principal.  The  statement  that  a  man 
borrowed  13000  at  6  %,  means  that  he  must  pay  6  %  of  iSOOO,  or 
$180,  each  year  for  the  use  of  the  $3000.  At  the  end  of  a  year  he 
would  owe  the  lender  13000  plus  the  interest  ($180),  or  $3180. 
The  sum  of  the  principal  and  the  interest  is  called  the  amount. 

220.  Promissory  Notes. 

It  is  the  custom  in  business  for  the  man  who  borrows  money  to 
give  a  written  promise  to  repay  the  sum  borrowed.  Such  a 
promise  is  called  a  promissory  note. 


'^o^ .A^%^,    O^^  ^7^  m 


■^c^rrr- 


^i/^yU^  ^.     <::^:^^^^^ 


/?//  ^:^^J^  ^^.;^^>>^^^  (Z,..i>^^^^J^^^:7^2^:^:Jt^  J^  ^  % 


^^    3  ^...^^^wv-^^   ^%.^^ 


S-^g^^g^^^^^^zx?^^ 


Promissory  Note 
257 


258  INTEREST 

If  the  borrower  is  a  person  of  small  means,  or  if,  for  any  other 
reason,  it  may  be  unsafe  to  loan  him  money,  he  may  be  requested 
to  have  some  person  of  recognized  financial  standing  sign  the  note 
with  him.  Such  notes  are  either  joint  notes,  or  joint  and  several 
notes,  depending  upon  the  wording. 


OO 


¥-00"^ .  ^m^6(or/e>.   >^/.  /,^^ m:S_ 


.^ 


'yj^^^  ^^..t^<^ y{:i/^di^!CMZl6^^^^y^^»^n^^^/tu^ 


^^fc^ffr  ~~~        <^^.^.  ^r^^,..^!^ 


S^_ ^^y ^iijAtW  TlfbuviiJlL 


taVSdtkAnjrarTft* 


Joint  and  Several  Note 


^^r7^A^yMe/^y:^/Y^yrf/^(Z^^  d  ^Zu^un^,  Mi^. 


Wif/iont  ffo/iilca/ffm,va/iw  received M'if/L  interest  ciyi^    (o  /^ 

/itr     ^^j2^  fu/dafknweor/ru>n'tffc/a/t/fioas/flet/,ca/^x'i^i!flffmpnt/i/fainsf  . .    iJ^t^tr'C^^ //x/i/  f/ny  /cmi  /i>rtfic 

oAmrsii/n  wM  /hsts/?/'siii/.andMamfys«>nmissu?n€/'  __^^L£:^hiy''l_. '  peroJit /or  cMc/mt  a//i/jr/ea.<rorfMon>rf,(f/u/m/At>u/ 
s/ayafejnHfiouMHlm/msi/wnanaaclaisimupffn^iwMyon/ra/e^^ 
orpeJWlM/■/^nvMr^y/wmh1ya/ldsa/conev/yexccutimAenvn,isais0AerrfyTxpnx^^/y^^r^m 
*uult>yv/r/MUH'aiiyfMin/>tMi/mvnoivm/^re.orwA/ckmayieAava/lerpd<!sfd.  ^ 

Witness ■t^i't^ hand  (ind  seal  /^^      tf^     iL^7±A'<L^ 


(SEAL) 


Judgment  Note 

221.    To  find  interest  at  6  %  for  6,  60,  600,  or  6000  days. 

The  interest  on  il  for  1  year  at  6  %  is  -f  .0(3 

The  interest  on  il  for  2  months  (60  da.)  is  .01 

The  interest  on  81  for  6  days  (^V  of  60  da.)  is     .001 

Thus,  to  find  the  interest  on  $1  for  60  days  at  6  %,  move  the 


INTEREST  259 

decimal  point  two  places  to  the  left ;  to  find  the  interest  for  6  days, 
move  the  point  three  places  to  the  left.  Since  this  is  true  if  the 
principal  is  i  1,  it  will  be  true  of  any  principal,  and  we  have  the 
following  rule : 

Given  any  principal,  to  find  the  interest  at  6  %. 

For  6  days,  move  the  decimal  point  three  places  to  the  left;  for  60  days, 
two  places  to  the  left ;  and  for  600  days,  one  place  to  the  left.  For  6000 
days  the  interest  will  he  the  same  as  the  principal. 

Oral  Work 

State  the  interest  on  each  of  the  following  principals  2itQ  foi  for 
6,  60,  600,  and  6000  days : 

1.  81000.  2.    1350.  3.    8125.60.'         4.   83620. 
5.   812.20.          6.    8325.50.         7.   $Q. 

m 

Find  the  interest  at  6  %  on : 
8.    8  245  for  6  days.  9.    8  27  for  6  days. 

10.    837.50  for  60  days.  ii.    812.50  for  6  days. 

222.  To  find  interest  at  6  %  for  fractions  or  multiples  of  6,  60, 
600,  or  6000  days. 

The  time  is  not  always  6,  60,  or  600  days,  yet  the  above  method 
can  be  easily  used  when  the  time  is  an  easy  fraction  or  an  exact 
multiple  of  6,  60,  600,  or  6000  days. 

Examples.     1.    Find  the  interest  on  8500  for  12  days  at  6  %. 

Solution.     $.50  =  the  interest  for  6  days. 

2  X  $  .50  =  $1,  the  interest  for  12  days. 

2.  Find  the  interest  on  8700  for  40  days  at  6  %. 

Solution.    |7  =  the  interest  for  60  days. 

?  of  $  7  =  1 4.67,  the  interest  for' 40  days. 
3 

3.  Find  the  interest  on  8  300  for  3  months  at  6  %, 

Solution.     $3  =  the  interest  for  2  months  (60  days). 
$3  H-  2  =  $1.50,  the  interest  for  1  month. 
$1.50  X  3  =  $4.50,  the  interest  for  3  months. 


260 


INTEREST 


Written  Work 

Rule  a  form  similar  to  the  following  model ;  compute  the  in- 
terest at  6  %  on  the  various  principals  for  the  different  times. 


Prin- 
cipals 


$125 

28 


146 
419 


25,000 


24  Da. 


30  Da. 

(1  Mo.) 


40  Da. 


Da. 


90  Da. 
(3  Mo.) 


18  Da. 


50  Da. 


70  Da. 


4  Mo. 


6  Mo. 


When  the  time  is  not  an  easy  fraction  or  an  exact  multiple  of 
6,  60,  or  600  days,  an  adaptation  of  the  method  shown  in  the  last 
exercise  may  be  used. 

Examples.     1.    Find  the  interest  on  $500  for  99  days  at  6  %. 

Solution.    ^  5.00  =  the  interest  for  60  days. 

2.50  =  the  interest  for  30  days. 

.50  =  the  interest  for    6  days. 

.25  =  the  interest  for  _3  days. 

$8.25  =  the  interest  for  99  days. 

2.    Find  the  interest  on  $1000  for  82  days  at  6  %. 

Solution.    $10.00    =  the  interest  for  60  days. 

3.33^  =  the  interest  for  20  days. 

.SS\  =  the  interest  for  _2  days. 

$13.67    =  the  interest  for  82  days. 


Oral  Work 

How  would  you  find  the  interest  on  any  principal  for  the  fol- 
lowing number  of  days  at  6  %  : 

3,        4,        5,        7,        8,        9,        36,        66,        69? 


INTEREST 


261 


Written  Work 

Enter  the  interest  at  6  %  in  the  proper  place  on  a  form  ruled 
like  the  following  model : 


10  da. 
66  da. 
63  da. 
6S  da. 
75  da. 
80  da. 
85  da. 
96  da. 
98  da. 
45  da. 
82  da. 
28  da. 


$  845.00 


$  632.00 


1 1296.00 


$5483.00 


$T4.60 


$  143.40 


1 746.95 


1 25.00 


$  130.00 


223.    To  find  interest  at  6  %  for  any  number  of  days. 

Sometimes   the   method    of   adding   the    interest  for  different 
fractions  or  multiples  of  6  and  60  days  cannot  conveniently  be  used. 
In  such  cases 

Point  off  three  places  in  the  principal;  this  will  give  the  interest 
for  six  days.  Multiply  by  the  number  of  days;  this  will  give  the 
interest  for  six  times  the  number  of  days.  Divide  by  six;  this  will 
give  the  interest  for  the  required  number  of  days. 

Example.     Find  the  interest  on  $500  for  19  days  at  6%. 

Solution*  %  .50  =  the  interest  for  6  dayg. 

$.50  X  19  =  $9.50,  the  interest  for  19  x  6  days. 
$9.50  -4-  6  =  $  1.58,  the  interest  for  19  days. 


Written  Work 

Enter  the  interest  at  6  %  on  the  various  principals  for  the  dif- 
ferent times  in  the  proper  place  on  a  form  ruled  like  the  following 
model: 


262     , 


INTEREST 


$435.00  $127.90  $213.65  $472.90  $123.60 


$12.35 


23  da. 

29  da. 

37  da. 

19  da. 

25  da. 

73  da. 

47  da. 

81  da. 
114  da. 

95  da. 

61  da. 

77  da. 
183  da. 
211  da. 


224.  Interchanging  Principal  and  Time.  There  is  a  short 
method  which  may  sometimes  be  used  when  the  days  are  not 
exact  multiples  of  6,  60,  600,  or  6000. 

The  interest  is  the  same  in  each  of  the  following  cases : 
1600.00  for  29  days  at  6%,  and 
$   29.00  for  600  days  at  6  %. 
It  is  much  easier  to  compute  the  interest  in  the  latter  case,  because 
all  that  is  necessary  is  to  point  off  one  place  in  the  principal,  giv- 
ing the  amount  of  interest  immediately,  $2.90. 

Therefore,  when  the  days  are  not  exact  multiples  or  easy  frac- 
tions of  6,  60,  600,  or  6000,  and  when  the  principal  is  an  exact 
multiple  or  easy  fraction  of  one  of  these  numbers,  interchange 
the  number  of  dollars  and  days,  and  proceed  as  before. 

Examples.     1.    Find  the  interest  on  $  360.00  for  83  days  at  6  % . 

Solution.     Interchanging,  we  have  $  83.00  for  360  days  at  6  %. 
Pointing  off  two  places,  f  .83  intere3t  for  60  days. 
Multiply  by  6  for  360  days,  and  the  result  is  $  4.98. 

2.    Find  the  interest  on  $  200.00  for  47  days  at  6  %. 

Solution.     Interchanging,  we  have  $47.00  for  200  days  at  6  %. 
Point  off  one  place  for  600  days,  $  4.70. 
Divide  by  3  for  200  days,  $  1 .57. 


INTEREST 


263 


Oral  Work 
How  would  you  find  the  interest  on  the  following  at  6  %  ? 
1.    $700.00  for  71  days.  2.    $150.00  for  59  days. 

3.    $420.00  for  113  days.  4.   130.00  for  57  days. 

5.    166.00  for  171  days.  6.    $1200  for  37  days. 

Written  Work 

Compute  and  enter  the  interest  at  6  %  on  a  form  ruled  like  the 
following  model : 


117  Da. 


34  Da. 


161  Da. 


59  Da. 


74  Da. 


3  Mo.  7  Da. 


$  300  00 
1200  00 

240  00 

420000 

150  00 

7200 

450  00 


54 
6000 
5000 


225.    To  find  the  interest  when  the  rate  is  other  than  6  %. 

First  find  the  interest  at  6^o,  then  take  \  of  the  result;  this  will  give 
the  interest  at  Ifc     Multiply  this  quotient  by  the  given  rate. 

The  following  short  methods  are  of  value  in  computing  interests 

If  the  rate  is  7  %,  add  i  of  the  interest  at  6  %. 

If  the  rate  is  5  %,  subtract  ^  of  the  interest  at  6  %. 

If  the  rate  is  7|  %,  add  -J  of  the  interest  at  6  %. 

If  the  rate  is  4^  %,  subtract  ^  of  the  interest  at  6  %. 


Oral  Work 


How  would  you  find  the  interest  at  4  %  ?  5^  %  ?  ^  %  ?  8  %  ? 


264 


INTEREST 
Written  Work 


Complete  the  following  blank  : 


Simple  Interest 


Rate 

36  Da. 

45  Da. 

63  Da. 

19  Da. 

47  Da. 

184  Da. 

2  Mo.  7  Da. 

$  436.50 

$75.80 

$174.30 

$  66.00 

$  1748.60 

$73.90 

$400.00 

6% 
8% 
5% 

226.  To  find  the  interest  when  the  time  is  stated  in  years, 
months,  and  days. 

In  the  preceding  problems  the  time  has  been  stated  in  days 
and  months.  When  the  time  has  been  stated  in  months,  we  have 
reduced  it  to  days,  but  when  the  time  is  stated  in  years,  months, 
and  days,  it  is  too  laborious  to  reduce  it  to  days,  and  the  follow- 
ing method  should  be  used. 

Find  the  interest  for  the  number  of  years  at  the  given  per  cent. 
To  this  result  add  the  interest  for  the  given  number  of  months  and 
days. 

Example  Find  the  interest  on  I  375  for  2  yr.  3  mo.  21  da. 
at  6%. 

Solution.     The  interest  for  1  yr.  is  5  %  of  the  principal. 
The  interest  for  2  yr.  is  10  %  of  the  principal. 
lO^o  of  $375=  137.50. 

The  interest  on  $375  for  3  mo.  21  da.  is  $5.78. 
.    Therefore,  the  interest  for  2  yr.  3  mo.  21  da.  is  $43.28. 


Written  Work 
Rule  a  blank  like  the  following  model.     Compute  and  enter  the 
interest. 


INTEREST 


265 


Complete  the  blank  : 


Simple  Interest 


Time 

$124.00 

$3T.62 

$1245 

.T5 

$463.80 

$2000.00 

Years 

Months 

Days 

6% 

5% 

3i% 

4% 

5^% 

1 

5 

24 

1 

8 

12 

2 

4 

18 

3 

8 

6 

4 

10 

12 

10 

2 

7 

8 

6 

2 

5 

7 

9 

3 

4 

15 

2 

7 

28 

3 

3 

20 

4 

7 

27 

9 

1 

19 

227.  To  compute  the  time  between  two  dates.  In  all  the  prob- 
lems given  thus  far,  the  time  has  been  stated.  You  will  often  be 
called  upon  to  compute  the  time.  In  such  cases  you  will  be  given 
the  date  when  the  note  was  made  and  the  date  when  it  is  due 
(date  of  maturity). 

There  are  two  methods  of  computing  the  time  between  dates : 

First  Method.  Counting  the  actual  number  of  days.  (Not 
used  if  the  interval  is  more  than  one  year.) 

Second  Method.  Compound  subtraction.  (May  be  used  for 
any  interval.) 

a.    To  find  the  time  by  counting  the  actual  number  of  days. 

Example.  Find  the  number  of  days  between  February  15, 1915, 
and  May  24,  1915. 

Solution.     February  has  28  days,  of  which  15  have  expired,  leaving 

in  February  13  days 

31  days 


March  has 

April  has 

The  note  matures  on  May 


Total 


30  days 

24 

98  days 


266  INTEREST 

From  this  problem  we  derive  the  following  rule : 

Add  the  number  of  days  remaining  in  the  month  after  the  day  the 
note  was  made^  the  exact  number  of  days  in  each  complete  month, 
and  the  number  of  days  through  which  the  note  is  to  run  in  the  last 
month. 

Written  Work 
Find  the  exact  number  of  days  between  the  dates  in  the  table  : 


Dub 

Made 

Oct.  26 

Nov.  13 

Dec.  27 

Jan.  3 

Jan.  17 

Feb.  26 

Oct.  13 
Sept.  27 
Aug.  18 
July  16 
July  3 
May  17 
May  1 

b.    To  find  the  interest  period  by  compound  subtraction  of  dates. 

Example.     Find  the  time  between  May  18,  1910,  and  February 
16,  1913. 


Solution.     1913 
1910 


16 
18 


Since  18  cannot  be  subtracted  from  16,  and  since  5  cannot  be  subtracted  from 
2,  reduce  1  month  to  days,  and  1  year  to  months. 

1912       13  46 

1910       _5  18 

2  yr.    8  mo.    28  da. 


Written  Work 


Find  the  time  by  compound  subtraction.  The  figures  in  the 
left-hand  column  are  the  dates  on  which  the  notes  were  given. 
The  dates  at  the  top  are  the  dates  of  maturity. 


INTEREST 


267 


To 

Fkom 

Matukity 

10-22-1913 

Maturity 
6-15-1914 

Maturity 
11-14-1914 

Maturity 
5-20-1915 

6-17-1913 

8-  5-1913 

9-25-1912 

11-  6-1912 

4-19-1910 

2-26-1909 

4-30-1912 

7-14-1913 

10-11-1906 

12-31-1912 

The  following  table  may  be  used  in  finding  the  exact  number  of 
days  between  any  two  dates  : 

For  illustration,  the  time  from  Apr.  7  to  Nov.  7  is  found  to  be 
214  da.  From  Sept.  3  to  Jan.  3  is  found  to  be  122  da.  To  find 
the  time  from  Sept.  3  to  Jan.  18,  add  15  da.  to  122  da. 


From  Any  Day 

To  THE  Same  Day  op  the  Next 

OF 

Jan. 

Feb. 

Mar. 

Apr. 

May 

June 

July 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

January      .     . 

365 

31 

59 

90 

120 

151 

181 

212 

243 

273 

304 

334 

February 

334 

365 

28 

59 

89 

120 

150 

181 

212 

242 

273 

303 

March    . 

306 

337 

365 

31 

61 

92 

122 

153 

184 

214 

245 

275 

April      . 

275 

306 

334 

365 

30 

61 

91 

122 

153 

183 

214 

244 

May.     . 

245 

276 

304 

335 

365 

31 

61 

92 

123 

153 

184 

214 

June 

214 

245 

273 

304 

334 

365 

30 

61 

92 

122 

153 

183 

July.     . 

184 

215 

243 

274 

304 

335 

365 

31 

62 

92 

123 

153 

August . 

153 

184 

212 

243 

273 

304 

334 

365 

31 

61 

92 

122 

September 

122 

153 

181 

212 

242 

273 

303 

334 

365 

30 

61 

91 

October . 

92 

123 

151 

182 

212 

243 

273 

304 

335 

365 

31 

61 

November 

61 

92 

120 

151 

181 

212 

242 

273 

304 

334 

365 

30 

December 

31 

62 

90 

121 

151 

182 

212 

243 

274 

304 

335 

365 

Review 

1.    In  the  following  exercise,  enter  the  time  (in  red  ink  ^)  on 

the  upper  of  the  two  lines,  and  the  interest  (in  black  ink)  on 

the  lower  line. 

1  At  teacher's  discretion. 


268 


INTEREST 


If  the  time  is  less  than  a  year,  compute  the  actual  number  of  days. 
If  the  time  is  more  than  a  year,  find  the  interval  by  compound 
subtraction,  and  state  it  in  years,  months,  and  days. 


Rate  6  % 

$216.80 

$  625.00 

$928.40 

$  87.86 

To 

9-29-1914 

11-26-1914 

12-24-1914 

1-26-1915 

9-22-1914 

6-24-1914 

4-  2-1914 

2-11-1914 

11-13-1913 

8-  6-1913 

5-22-1913 

4-25-1912 

7-13-1910 

2.    Complete  the  follqwing,  entering  the  time  on  the  upper  of 
the  two  lines,  and  the  interest  on  the  lower. 


5% 

4i% 

7% 

Ti% 

Fkoh 

To 

May  26,  1914 

Aug.  17,  1914 

Oct.  9,  1914 

Feb.  10,  1915 

Principal,  $219.80 

April  22,  1914 

Principal,  1326.00 

May  17,  1914 

Principal,  $80.00 

September  19,  1913 

Principal,  $260.00 

May  14,  1913 

' 

INTEREST  269 

Written  Review 
Use  the  simplest  method  to  find  the  interest  on  the  following : 
1.    Interest  at  6%  on  1321.65  for  24  da. 
;2.    Interest  at  6  %  on  $523.19  for  20  da. 

3.  Interest  at  6  %  on  $413.00  for  75  da. 

4.  Interest  at  6  %  on  1300.00  for  57  da. 

5.  Interest  at  5%  on  $450.00  for  35  da. 

6.  Interest  at  7^  %  on  $216.80  for  42  da. 

7.  Interest  at  4  %  on  $625.00  for  117  da. 

8.  Interest  at  6  %  on  $80.00  for  3  yr.  8  mo.  15  da. 

9.  Interest  at  6  %  on  $50.00  from  March  24,  1914,  to  May  26, 
1914. 

10.  Interest  at  7  %  on  $125.00  from  July  19,  1911,  to  January 
14,  1915. 

228.  Accurate  Interest.  The  methods  of  computing  interest 
already  explained  are  based  on  the  assumption  that  a  year  con- 
tains 360  days.  The  slight  error  is  ignored  because  of  the  con- 
venience of  the  method.  However,  the  United  States  government 
and  some  business  houses  prefer  to  use  exact  interest. 

When  we  compute  interest  on  a  basis  of  360  days  to  the  year, 
we  ignore  5  days.  Five  days  are  3 1^  or  y^^  of  a  year.  When,  for 
example,  we  call  180  days,  \\^  or  ^  a  year,  we  obtain  a  result 
which  is  Y^^  too  large.  Since  accurate  interest  is  y^^  smaller  than 
the  interest  computed  by  the  simple  methods,  we  can  find  accurate 
interest  by  the  following  rule : 

To  find  accurate  interest. 

Find  the  interest  hy  one  of  the  common  methods;  diminish  this 
result  hy  -^-^  of  itself. 

Example.  What  is  the  accurate  interest  on  $3500.00  for  15 
days  at  6  %  ? 

Solution.     $35.00  is  the  interest  for  60  days. 

J$  35.00  H-  4  =  $8.75,  the  interest  for  15  days. 

7Vof$8.75  =  $.12. 

$8.75  -  $.12  =  $8.63,  the  accurate  interest. 


270  INTEREST 

Written  Work 
Find  the  accurate  interest  on  the  following: 

1.  1584.00  for  24  days  at  6%. 

2.  f  275.00  for  84  days  at  6  %. 

3.  123.75  for  IIB  days  at  5%. 

4.  165.80  for  2  months  12  days  at  6%. 

5.  1138.50  for  9  months  16  days  at  7%. 

229.  To  find  the  time.  Situations  sometimes  arise  in  which  it  is 
necessary  to  determine  the  time,  when  the  principal,  the  rate,  and 
the  interest  are  known. 

Oral  Work 

The  interest  on  $250.00  for  6  days,  at  6%,  is  1.25.  f  1.00  is 
the  interest  for  how  many  days  at  6  %  ? 

The  interest  on  $1200  for  1  day  at  6  %  is  1.20.  14.40  is  the 
interest  for  what  length  of  time  at  6  %  ? 

From  these  problems  the  following  rule  will  be  understood. 

To  find  the  time  when  the  principle,  rate,  and  interest  are  known. 

Find  the  interest  on  the  given  principal  at  the  given  rate  for  one 
dag.  Divide  the  total  interest  by  the  interest  for  one  day  to  determine 
the  number  of  days. 

Example.  The  interest  on  $4500.00  at  6  %  for  a  certain  time  is 
$10.50.     What  is  the  time  ? 

Solution.     The  interest  on  $4500.00  for  1  day  at  6  %  is  |  .75. 
$  10.50  -f-  $  .75  =  14,  the  number  of  days. 

Written  Work 
Find  the  time  in  each  of  the  following : 

Principal  Rate  Interest  Timb 

1.  $  360.00  6%  $  1.62 

2.  $1500.00  6%  I  9.75 

3.  $1473.00  6%  $22.59 

4.  $  279.80  6%  $  1.91 

5.  $  176.90  5%  $  2.82 


INTEREST  271 

230.    To  find  the  principal. 

The  interest  on  11.00  for  72  days  at  6%  is  1 .012.  $.24  is  the 
interest  on  how  many  dollars  for  72  days  at  6  %  ? 

To  find  the  principal  when  the  rate,  the  time,  and  the  interest  are 
known. 

Find  the  interest  on  $1.00  for  the  given  time  at  the  given  rate. 
Divide  the  given  interest  hy  the  interest  on  $1.00  to  determine  the 
principal.  , 

Example.  The  interest  on  a  certain  principal  at  6  %  for  54 
days  is  $2.48.     What  is  the  principal? 

Solution.    The  interest  on  $  1.00  for  54  days  at  6%  is  |  .009. 

$2.48  -4-  $  .009  =  275.56,  the  number  of  dollars  in  the  principal 


Written  Work 

Find  the  principal 

in  each  of  the  following : 

Time 

Ratb 

INTBBEST 

Pbincipal 

1.    75  days 

6% 

$  3.36 

2.    35  days 

6% 

1  1.67 

3.    92  days 

5% 

$     .52 

4.    72  days 

6% 

$21.60 

5.    90  days 

5% 

$45.00 

6.    60  days 

6% 

$  1.00 

7.    30  days 

7% 

$  1.40 

8.   90  days 

6% 

$13.50 

231.    To  find  the  rate  when  the  principal,  the  interest,  and  the 
time  are  given. 

Find  the  interest  on  the  given  principal  for  the  given  time  atl%. 
Divide  the  total  interest  hy  the  interest  at  1  %  to  find  the  rate. 

Example.     The  interest  on  $1500.00  for  30  days  at  a  certain 
rate  is  $6.25.     What  is  the  rate? 

SoLUTiox.     The  interest  on  »|  1500.00  for  30  days  at  1  %  is  $  1.25. 
^6.25  -H  $  1.25  =  5,  the  rate  per  cent. 


^2 

INTEREST 

Written  Work 

Find  the  rate  in  each  of  the  following : 

Pkincipal 

Time 

Interest 

1.    $1375.00 

42  days 

i   9.63 

2.    1  876.25 

95  days 

$11.56 

3.    $  694.75 

27  days 

$  3.65 

4.    $  940.00 

2  yr.  6  mo. 

894.00 

Bats 


232.  Periodic  Interest.  Periodic  interest  is  the  simple  interest 
on  the  principal,  plus  the  simple  interest  on  each  irstalhnent  of 
interest  which  was  not  paid  when  due.  The  interest  on  the  prin- 
cipal may  be  due  at  any  stated  interval,  usually  quarterly,  semi- 
annually, or  annually. 

Periodic  interest  is  not  legal  in  some  states.  Special  contracts 
are  sometimes  made  which  provide  for  its  payment. 

Example.  What  is  the  periodic  interest  on  a  loan  of  $5000.00 
at  6  %  for  1  yr.  6  mo.,  interest  due  quarterly  ? 

Solution.  The  simple  interest  on  $  5000.00  for  1  yr.  6  mo.  at  6  9^o  is  $  450.00. 
The  first  interest  payment  of  $  75  is  due  at  the  end  of  3  mo., 

and  remains  unpaid  for  1  yr.  3  mo. 

The  second  interest  payment  is  due  in  6  mo.  and  is  unpaid  for  1  yr. 

The  third  interest  payment  is  due  in  9  mo.  and  is  unpaid  for  9  mo. 

Fourth  interest  payment  is  unpaid  for  6  mo. 

Fifth  interest  payment  is  unpaid  for  3  mo. 

The  sixth  interest  payment  is  due  at  the  maturity  of  the  note, 

and  is  paid  when  due. 
The  total  time  during  which  interest  payments  remain  unpaid  is        3  yr.  9  mo. 

The  interest  on  $75.00  for  3  yr.  9  mo.  at  6  %  is    1 16.88 

Simple  interest  on  the  principal  =  $  450.00 

Interest  on  unpaid  interest  =       16.88 

Periodic  interest  =  $466.88 

The  amount  due  at  the  end  of  1  yr.  6  mo.  (principal  and  interest)  is 
$5466.88. 

Written  Work 

Complete  a  form  ruled  like  the  following  model.  The  results 
in  the  illustration  are  entered  in  the  first  column  to  illustrate  how 
to  fill  in  the  various  blanks. 


INTEREST 


273 


Principal  $5000 
Rate  6  % 
Time  1  Yr.  6  Mo. 
Int.  Due  Quarterly 

Principal  $2000 
Rate  6% 
Time  2  Yk.  3  Mo. 
Int.  Due  Quarterly 

Principal  $1200 

Rate  6  % 

Time  4  Yr. 

Int.  Due  Semi-annually 

Principal  $1700 

Rao'e  ()  % 

Time  6  Yr.  6  Mo. 

Int.  Due  Semi-annually 

Principal  $6500 
Rate  7  % 
Time  1  Yr.  9  Mo. 
Int.  Due  Quarterly 

Principal  $1500 

Rate  5% 

Time  2  Yr. 

Int.  Due  Annually 

Principal  $3000 

Rate  8% 

Time  4  Yr. 

Int.  Dub  Quarterly 

Simple  interest  .     .     . 

$    450.00 

Amount  of  each  inter- 
est payment    .     .     . 

75.00 

Sum  of  periods  interest 
is  unpaid    .... 

3  yr.  9  mo. 

Interest  on  unpaid  in- 
terest      

$      16.88 

Total  interest      .     .     . 

466.88 

Amount    of    note     at 
maturity     .... 

5466.88 

CHAPTER   XXV 
PARTIAL  PAYMENTS 

Part  payment  of  an  interest-bearing  debt  is  known  as  a  "  partial 
payment."  Such  payments  should  be  recorded  on  the  back  of  the 
note. 

One  of  the  following  methods  is  usually  employed  in  computing 
the  balance  remaining  after  partial  payments  have  been  made. 

233.  The  United  States  Rule.  The  United  States  Rule  has 
been  approved  by  the  Supreme  Court  of  the  United  States,  and  is 
usually  employed  when  the  time  of  the  interest- bearing  debt 
exceeds  one  year.     This  method  provides  that : 

a.  Payments  must  be  applied  to  pay  accrued  interest  before  any 
deduction  can  be  made  from  the  principal. 

h.  Payments  which  do  not  pay  the  accrued  interest  leave  the 
principal  undiminished  until  other  payments  are  made  which  are 
sufficient  to  cover  all  accrued  interest. 

c.  Any  surplus  remaining  after  accrued  interest  is  paid  in  full 
is  applied  toward  the  reduction  of  the  principal. 

Partial  payments  may  be  made  only  by  agreement  between  the 
maker  and  the  payee.     This  agreement  may  appear  in  the  note. 


^//^nn^-^ (:^yl^J^/^,j4i^7't.<'^ytY  /6  J^/.^ 


hyjf^.^^^^^, —      y7/;^J////7//y<^ /lM//fMfyye//A 


rA^^^  0<^/^:^^j^yr . 


0..^^g^C^>^<8^^  £^/^^^^^^^^       f 


ya^.^A<^^.'i?^//t^c^..<^^4^y^<.^^  ^  <^  7^ 


^^         ^  ^.y^AJ.,^^6  /^/6       "^     0^^.^^_ 


274 


PARTIAL  PAYMENTS 


275 


The  above  note  had  the  following  indorsements,  showing  pay- 
ments made  with  the  consent  of  the  payee. 


Example.  What  amount  w^as  necessary  to  pay  the  note  and 
interest  at  maturity? 

Solution.     Time  from  January  16,  1913,  to  March  10,  1913,  1  mo.  24  da. 

Interest  on  $1800.00  for  1  mo.  24  da.  is  $16.20. 

1200.00  (first  payment)  -$16.20  (accrued  interest)  =$  183.80,  surplus  to 
apply  on  principal. 

$  1800.00  -  %  183.80  =  %  1616.20,  unpaid  principal. 

Time  from  March  10,  1913,  to  April  13,  1914,  is  1  yr.  1  mo.  3  da. 

Interest  on  $  1616.20  for  1  yr.  1  mo.  3  da.  is  %  105.86. 

The  payment  of  %  75.00  does  not  cover  the  accrued  interest,  and  the  principal 
therefore  remains  undiminished. 

Time  from  April  13,  1914,  to  August  13,  1915,  is  1  yr.  4  mo. 

Interest  on  $  1616.20  for  1  yr.  4  mo.  is  %  129.30. 

$105.86  +  $129.30  =  $235.16,  total  accrued  interest. 

$  75.00  +  $  500.00  =  $  575.00,  total  payments. 

$575.00  —  $235.16  =  $339.84,  surplus  remaining  to  apply  on  principal. 

$1616.20  -  $339.84  =  $  1276.36,  unpaid  principal. 

Time  from  August  13,  1915,  to  January  16,  1916,  is  5  mo.  3  da. 

Interest  on  $  1276.36  for  5  mo.  3  da.  is  $32.55. 

$1276.36  -f  $  32.55  =  $1308.91,  amount  required  to  pay  principal  and  accrued 
interest  at  maturity. 

The  work  may  be  arranged  in  tabular  form,  as  shown  by  the 
following  illustration  : 


276 


PARTIAL  PAYMENTS 


Partial  Payments  on  a  Note  Computed  by  the  United  States  Rule 


Accrued  Interest 

Datk 

Time 

Amount 

Payment 

APPLY   ON 

Principal 

Principal 

Yr. 

Mo. 

Da. 

Of  Note,  1913-1-16 
1st  Payment,  1913-3-10 

1 
1 

1 
1 

4 

5 

24 
3 
0 

3 

16 

20 

200 

00 

183 
339 

80 
84 

1800 
1616 

1276 
1308 

A.mount 
at  matu 

00 
20 

2d  Payment,  1914  4  13 
3d  Payment,  1915-8-13 

105 
129 

86 
30 

75 
500 

00 
00 

235 

16 

575 

00 

36 

Maturity,  1916-1-16 

32 

55 

91 

due 
rity 

234.  The  Merchants'  Rule.  The  Merchants'  Rule  is  generally 
used  by  banks  and  by  business  men  to  find  the  balance  due  when 
partial  payments  are  made  on  interest-bearing  notes  in  which  the 
time  is  one  year  or  less.     It  provides  that : 

a.  The  principal  shall  draw  interest  from  the  date  the  loan 
is  made  until  the  date  of  the  final  settlement. 

b.  Each  payment  shall  draw  interest  from  the  date  the  pay- 
ment is  made  until  the  final  settlement. 

Example.  On  a  note  of  $500.00,  dated  July  8, 1914,  payable  in 
one  year  with  interest  at  6  %,  the  following  payments  were  made : 
Sept.  15, 1914,  $200.00;  Jan.  8,1915,  $150.00;  May  8, 1915,  $60.00. 
What  amount  was  necessary  to  make  final  settlement  on  July  8,1915? 

Solution.     Principal 

Int.  on  %  500.00  for  1  yr.  at  6% 

Total 
First  payment 
Int.  on  first  payment  from  9-15-14  to  7-8-15 

Total 
Second  payment 
Int.  on  second  payment  from  1-8-14  to  7-8-15 

Total 
Third  payment 
Int.  on  third  payment  from  5-8-14  to  7-8-15 

Total 
Sum  of  payments  and  interest 
Balance  due  July  8,  1915 


$500.00 

30.00 

$530.00 

1200.00 

9.78 

$209.78 

$150.00 

4.50 

154.50 

$60.00 

.60 

60.60 

424.88 

$105.12 


PARTIAL  PAYMENTS 


277 


This  work  may  be  arranged  in  tabular  form  as  shown  in  the 
following  illustration : 

Tabular  Form  for  Indicating  Results  of  Partial  Payments 
Computed  by  the  Merchants'  Rule 


Loan 

Partial  Payments 

Dates 

Princi- 
pal 

Interest 

Amount 

Pay- 
ment 

Interest 

Amount 
of  Pay- 

Time 
mo.     da. 

Dollars 

ment  and 
Interest 

Of  note 
Maturity 
First  payment 
Second  payment 
Third  payment 

7-8-1914 
7-8-1915 
9-15-1914 
1-8-1915 
5-8-1915 

500 

00 

30 

00 

530 
530 

00 
00 

200 

150 

60 

Bal. 

00 
00 
00 

due 

9 
6 

2 

atfi 

25 
0 
0 

nal 

9 
4 

settl' 

78 
50 
60 

m't 

209 
154 
60 
424 
105 
530 

78 
50 
60 
88 

12. 

00 

Written  Work 

The  first  two  problems,  being  for  long-time  loans,  should  be 
computed  by  the  United  States  Rule.  Prepare  a  ruled  form 
similar  to  the  model  and  show  your  results  thereon.  In  each 
problem,  find  the  balance  due  at  maturity. 

1.    Principal,  14000.00. 

Date  of  paper,  November  16,  1916. 

Time,  4  yr. 

Rate,  6%. 

Payments : 


Jan. 

20,  1917,  $     75.00 

Sept. 

26,  1917, 

125.00 

Apri] 

5,  1918, 

500.00 

Oct. 

21,  1918, 

100.00 

July 

10,  1919, 

250.00 

Oct. 

21,  1919, 

1500.00 

278  PARTIAL  PAYMENTS 

2.    Principal,  -11200.00. 
•   Date  of  paper,  October  29,  1917. 
Time,  2  yr.  6  mo. 
Rate,  6%. 
Payments : 


Jan.      16,1918, 

$  60.00 

Nov.       6,  1918, 

25.00 

March  12,  1919, 

165.00 

July     10,  1919, 

15.00 

Sept.     28,  1919, 

150.00 

Dec.        3,  1919, 

275.00 

The  following  problems,  being  for  short-time  loans,  should  be 
computed  by  the  Merchants'  Rule.  Rule  a  form  similar  to  the 
model. 

3.    Principal,  8600.00. 

Date  of  paper,  September  15,  1917. 

Time,  1  yr. 


Rate,  6%. 
Payments : 


Oct.  20,  1918,  $  75.00 
Nov.  11,  1918,  60.00 
Feb.  16,  1919,     115.00 


4.    Principal,  #1000.00. 

Date  of  paper,  March  19,  1917, 

Time,  6  mo. 

Rate,  5%. 

Payments : 


April  21,  i  65.00 
May  27,  125.00 
June  24,  180.00 
Aug.  19,     200.00 


CHAPTER   XXVI 
CX)MPOUND  INTEREST 

235.  Compound  Interest.  Compound  interest  is  interest  com- 
puted, at  regular  intervals,  on  the  sum  of  the  principal  and  any  un- 
paid interest.  In  other  words,  as  soon  as  interest  becomes  due  and 
is  unpaid,  it  begins  to  draw  interest  at  the  same  rate  as  the  princi- 
pal. Compound  interest  is  generally  paid  on  the  deposits  in  savings 
banks  and  is  used  in  calculating  sinking  funds. 

Interest  may  be  compounded  quarterly,  semi-annually,  annually, 
or  at  the  end  of  any  other  period  agreed  upon.  In  some  states 
the  collection  of  compound  interest  is  not  permitted. 

Example.  Find  the  amount  and  the  compound  interest  of 
11200  at  6%  for  two  years,  interest  compounded  semi-annually. 

Solution.    |  1200.00  First  principal 

36.  Interest  for  6  months 

1236.  Principal  at  beginning  of  second  6-months  period 

37.08  Interest  for  second  6  months 


1273.08  Principal  at  beginning  of  third  period 

38.19  Interest  for  third  period 

1311.27  Principal  at  beginning  of  fourth  period 

39.34  Interest  for  fourth  period 

$  1350.61  Amount  at  end  of  two  years 

f  1350.61  Amount  at  end  of  two  years 

1200.00  Principal 

$  150.61  Compound  interest 

Written  Work 

1.  Find  the  compound  interest  on  i  500. 00  for  5  years  at  6  %, 
interest  compounded  annually. 

2.  What  is  the  amount  and  the  compound  interest  on  $7500.00 
loaned  for  3  years  at  6%,  interest  compounded  semi-annually? 

3.  Find  the  interest  on   $1200.00  loaned   for  2  years  at  5% 
compound  interest,  interest  compounded  quarterly. 

279 


280 


COMPOUND   INTEREST 


Compound  interest  is  computed  with  much  less  work  by  the  use 
of  tables  showing  the  accumulation  of  interest  and  principal 
when  $1.00  is  loaned  at  compound  interest. 

236.    Compound  Interest  Table. 

Showing  the  amount  of  |1.00  compounded  annually  at  various  rates 


Yeaes 

1% 

U% 

2% 

2i% 

3% 

Si% 

4% 

4i% 

5% 

6% 

Years 

1 

0.010000 

1.005000 

1.020000 

1.025000 

1.030000 

1.085000 

1.040000 

1.045000 

1.050000 

1.060000 

1 

2 

1.020100 

1.030225 

1.040400 

1.050625 

1.060900 

1.071225 

1.081600 

1.092025 

1.102500 

1.123600 

2 

3 

1.030301 

1.045678 

1.061208 

1.076891 

1.092727 

1.108718 

1.124864 

1.141166 

1.157625 

1.191016 

8 

4 

1 ,040604 

1.061364 

1.082482 

1.103818 

1.125509 

1.147528 

1.169859 

1.192519 

1.215506 

1.262477 

4 

5 

1.051010 

1.077284 

1.104081 

1.131408 

1.159274 

1.187686 

1.216658 

1.246182 

1.276282 

1.338226 

5 

6 

1.061520 

1.093443 

1.126162 

1.159693 

1.194052 

1.229255 

1.265319 

1.302260 

1.340096 

1.418519 

6 

7 

1.072135 

1.109845 

1.148686 

1.188686 

1.229874 

1.272279 

1.815932 

1.360862 

1.407100 

1.503630 

7 

8 

1.082857 

1.126493 

1.171659 

1.218403 

1.266770 

1.316809 

1.868569 

1.422101 

1.477455 

1.59384S 

8 

9 

1.093685 

1.143390 

1.195093 

1.248863 

1.304778 

1.862897 

1.423312 

1.486095 

1.551328 

1.689479 

9 

10 

1.104622 

1.160541 

1.218994 

1.2S00S5 

1.843916 

1.410599 

1.480244 

1.552969 

1.628895 

1.790848 

10 

11 

1.115668 

1.177949 

1.248874 

1.812087 

1.384284 

1.459970 

1.539454 

1622853 

1.710839 

1.898299 

11 

12 

1.126825 

1.195618 

1.268242 

1.344889 

1.425761 

1.511069 

1.601032 

1.6958S1 

1.795856 

2.012197 

12 

13 

1.138093 

1.213552 

1.293607 

1.378511 

1.468584 

1.563956 

1.665074 

1.772196 

1.885649 

2.132928 

13 

14 

1.149474 

1.231756 

1.319479 

1.412974 

1.512590 

1.618695 

1.731676 

1.851945 

1.979932 

2.260904 

14 

15 

1.160969 

1.250232 

1.345868 

1.448298 

1.55T967 

1.675849 

1.800944 

1.985282 

2.078928 

2.896558 

15 

16 

1.172579 

1.268986 

1.372786 

1.484506 

1.604700 

1.788986 

1.872981 

2.022870 

2.182875 

2.540352 

16 

17 

1.184304 

1.288020 

1.400241 

1.521618 

1.C52848 

1.794676 

1.947901 

2.118877 

2.292018 

2.692778 

17 

18 

1.196148 

1.807341 

1.428246 

1.559659 

1.702488 

1.8574S9 

2.025817 

2.208479 

2.406619 

2.854839 

18 

19 

1.208109 

1.826951 

1.456811 

1.598650 

1.758506 

1.922501 

2.106849 

2.307860 

2.526950 

3.025600 

19 

20 

1.220190 

1.846855 

1.485947 

1.688616 

1.806111 

1.989789 

2.191128 

2.411714 

2.653298 

3.207186 

20 

21 

1.232392 

1.867058 

1.515666 

1.679582 

1.860295 

2.059481 

2.278768 

2.520241 

2.785968 

3.399564 

21 

22 

1.244716 

1.887564 

1.545980 

1.721571 

1.916103 

2.131512 

2.369919 

2.633652 

2.925261 

3.603537 

22 

23 

1.257168 

1.408377 

1.576899 

1.764611 

1.973587 

2.206114 

2  464716 

2.752166 

8.071524 

3.819750 

28 

24 

1.269735 

1.429503 

1.608437 

1.808726 

1.082794 

2.283328 

2.563304 

2.876014 

3.225100 

4.048935 

24 

25 

1.282432  1.450945 

1.640606 

1.853944 

1.093778 

2.363245 

2.665886 

3.005484 

3.386355 

4.291871 

25 

Example.  Find  the  compound  interest  on  $3562.80  for  4 
years  at  6  %,  interest  compounded  annually. 

Solution.  $  1.00  compounded  annually  at  6  %  for  4  years  amounts  to 
$  1.262477,  as  shown  by  the  table. 

3562.80  X  $1.262477  =  $4497.95,  amount  of  $3562.80  compounded  annually 
for  4  years  at  6  %. 

$4497.95  -  $3562.80  =  $935.15,  compound  interest. 

When  interest  is  compounded  semi-annually,  take  |  the  rate 
for  twice  the  time. 


COMPOUND  INTEREST  281 

When  interest  is  compounded  quarterly,  take  ^  the  rate  for 
4  times  the  time. 

Example.  What  is  the  compound  interest  on  $  5000.00  at  8  % 
for  3  years  6  months,  interest  compounded  quarterly  ? 

Solution.    ^oiS%  =  2%. 

4  times  3  years  6  mo.  =  14  years. 

The  amount  of  $  1.00  compounded  at  2%  for  14  years  is  11.319479. 

5000  X  II. 319479  =  1 6597.40. 

$6597.40  -  15000.00  =  11597.40,  compound  interest. 

Written  Work 

1.  Find  the  compound  interest  on  !$  2500. 00  for  5  years  at  5%, 
interest  compounded  annually. 

2.  i 5000. 00  was  invested  at  4%,  interest  compounded  semi- 
annually.    To  what  sum  did  this  investment  amount  in  7  years  ? 

3.  What  was  the  compound  interest  on  a  loan  of  f  3750.00,  made 
June  1,  1909,  and  due  December  1,  1914,  at  6%,  interest  com- 
pounded quarterly  ? 

4.  What  sum  must  be  invested  at  5  %  compound  interest  to 
amount,  in  7  years,  to  $3249.84,  if  the  interest  is  compounded 
semi-annually  ? 


CHAPTER   XXVII 

SAVINGS   BANKS 

237.  Checking  and  Savings  Accounts.  Most  banks  receive  de- 
posits  under  two  classes  of  accounts,  checking  accounts  and 
savings  accounts. 

Money  deposited  in  checking  accounts  can  be  drawn  out  by 
checks  payable  to  the  depositor  or  to  any  other  party.  These 
checks  are  payable  on  presentation  at  the  bank.  The  cash  on 
deposit  usually  does  not  bear  interest. 

Money  deposited  in  a  savings  account  cannot  be  drawn  out  by 
a  check  payable  to  any  person  other  than  the  depositor  himself. 
The  law  usually  provides  that  the  bank  may  require  notice  of 
from  10  to  60  days  before  paying  money  from  a  savings  account. 
Banks  rarely  take  advantage  of  this  privilege,  however.  The 
cash  on  deposit  bears  interest  at  some  rate  fixed  by  the  bank. 
8%,  3J%,  and  4%  are  common  rates. 

238.  Computing  Interest  on  Savings  Accounts.  Interest  is  com- 
puted on  the  smallest  balance  which  the  depositor  leaves  in  the 
bank  during  the  entire  time  between  fixed  days.  These  fixed 
days  are  called  interest  days,  and  the  time  between  the  interest 
days  is  called  the  interest  term. 

Some  banks  pay  interest  on  dollars  only,  and  ignore  the  cents. 
Interest  which  is  not  withdrawn  by  the  depositor  is  added  to  his 
account,  and  draws  interest  the  same  as  a  deposit.  Thus,  savings 
banks  really  pay  compound  interest. 

Example.  The  interest  days  of  the  Snowden  Savings  Bank  are 
January  1,  April  1,  July  1,  and  October  1.  On  each  of  these 
interest  days,  interest  at  the  rate  of  4%  per  annum  is  computed 
on  the  smallest  quarterly  balance.  The  account  of  W.  M.  Scott  is 
shown  on  the  following  page. 

282 


SAVINGS  BANKS 


283 


W.  M.  Scott 


Date 

Deposits 

Intekest 

Withdrawals 

Balance 

1915 

Feb. 

7 

120 

00 

120 

00 

April 

20 

300 

00 

420 

00 

April 

30 

100 

00 

320 

00 

July 

1 

1 

20 

321 

20 

July 

15 

50 

00 

371 

20 

Sept. 

17 

75 

00 

446 

20 

Oct. 

1 

3 

21 

449 

41 

Nov. 

16 

80 

00 

369 

41 

1916 

Jan. 

1      1 

1 

3 

i 

69 

373 

10 

Explanation.  The  first  interest  term  was  from  Jan.  1  to  April  1,  but 
since  Mr.  Scott  made  no  deposit  until  Feb.  7,  the  smallest  balance  on  deposit 
during  the  entire  interest  term  was  $  0.00,  and,  therefore,  no  interest  was  added 
on  April  1. 

The  second  interest  term  was  from  April  1  to  July  1.  The  smallest  balance 
on  deposit  during  the  entire  term  was  $120.00  (the  balance  on  April  1). 
Interest,  $  1.20. 

The  third  interest  term  was  from  July  1  to  Oct.  1.  Smallest  balance, 
1321.20.     Interest,  $3.21. 

The  fourth  interest  term  was  from  Oct.  1  to  Jan.  1.  Smallest  balance, 
$369.41.     Interest,  $3.69. 

239.  Interest  Terms  and  Dates  of  Adding  Interest.  Interest 
terms  are  not  of  uniform  length  among  the  various  banks  of  the 
country.  Some  banks  compute  interest  on  monthly  balances, 
some  on  quarterly  balances,  and  some  on  semi-annual  balances. 

Some  banks  add  interest  quarterly  and  some  add  it  semi- 
annually. The  rules  applying  to  the  interest  computations  of  any 
bank  may  usually  be  found  in  the  by-laws  of  the  bank,  printed  in 
the  depositor's  pass  book. 


Examples.  1.  Suppose  the  Snowden  Savings  Bank  computed 
interest  on  quarterly  balances,  but  added  interest  semi-annually. 
W.  M.  Scott's  account  would  appear  as  follows  : 


284 


SAVINGS  BANKS 
W.  M.  Scott 


Date 

Deposits 

Interest 

Withdrawals 

Balance 

1915 

Feb. 

7 

120 

00 

20 

00 

April 

20 

300 

00 

420 

00 

April 

30 

100 

00 

320 

00 

July 

1 

1 

20 

321 

20 

July 

15 

50 

00 

371 

20 

Sept. 

17 

75 

00 

446 

20 

Nov. 

16 

80 

00 

366 

20 

1916 

Jan. 

1 

6 

87 

373 

07 

Explanation. 


Smallest  Balance 

Quarterly 
Interest 

Semi-annual 
Dividend  of  Int 

First  Quarter        $     0.00 

10.00 

Second  Quarter      120.00 

1.20 

$1.20 

Third  Quarter         321.20 

3.21 

Fourth  Quarter       366.20 

3.66 

6.87 

2.  Suppose  the  Snowden  Savings  Bank  computed  interest  on 
the  monthly  balance  and  added  interest  quarterly.  Scott's  ac- 
count would  appear  as  follows : 

Explanation. 


Month 

Monthly  Balance 

1  Month  Interest 

i0Fl% 

Quarterly  Dividend 
OF  Interest 

Feb 

1000 

00 

$0 

00 

March 

120 
120 

00 
40 

40 

$0 

40 

April 

40 

May 

320 

40 

06 

June 

320 
322 

40 
92 

06 

2 

52 

July 

^ 

07 

Aug 

372 

92 

24 

Sept 

372 
451 

92 
47 

24 

3 

55 

Oct 

50 

Nov 

371 

47 

23 

Dec 

371 

47 

23 

3 

96 

SAVINGS  BANKS  •  285 

In  computing  interest  on  savings  accounts,  cents  in  the  principal 
are  dropped.     Fractions  of  cents  in  interest  are  dropped. 

Written  Work 

1.  Check  the  computations  in  each  of  the  illustrations  above. 

2.  Prepare  W.  IVl.  Scott's  account  on  the  supposition  that  the 
bank  computes  interest  on  monthly  balances  and  adds  interest 
semi-annually,  Jan.  1  and  July  1. 

3.  Prepare  W.  M.  Scott's  account  on  the  supposition  that  the 
bank  computes  interest  on  semi-annual  balances  and  adds  interest 
semi-annually.  Remember  that  interest  is  paid  on  the  smallest 
balance  on  deposit  during  the  entire  interest  term. 

4.  Which  of  the  methods  employed  in  this  section  is  most 
profitable  for  the  depositor? 

5.  Suppose  you  deposited  i  30  in  a  savings  bank  and  left  it  to 
draw  compound  interest  for  5  years  at  4%,  interest  compounded 
semi-annually.  How  much  could  you  withdraw  at  the  end  of  the 
fifth  year? 

6.  Suppose  you  had  loaned  the  830  for  5  years  at  4%  simple 
interest.     What  would  the  interest  have  been  for  five  years  ? 

7.  Compare  the  simple  and  compound  interest  in  Problems  5 
and  6. 

8.  A  man  deposits  f  1200  in  a  savings  bank  to  be  used  to  send 
his  boy  to  college.  The  savings  bank  pays  4%  interest,  com- 
pounded semi-annually.  The  deposit  was  made  on  the  boy's  tenth 
birthday.  What  amount  will  he  have  to  his  credit  on  the  boy's 
eighteenth  birthday  if  no  withdrawals  and  no  other  deposits  are 
made? 

9.  Make  accounts  with  D.  O.  Dorman  ;  one  for  each  of  the 
following  methods  of  declaring  interest.     Rate  4%. 

a.  Interest  computed  on  monthly  balances.  Dividends  added 
Jan.  1,  April  1,  July  1,  and  Oct.  1. 

h.  Interest  computed  on  quarterly  balances.  Interest  days 
same  as  above. 


286 

SAVINGS  BANKS 

c.  Interest  computed 

on 

quarterly 

balances. 

Dividends  added 

Jan.  1  and  July  1. 

Date 

Deposits 

Withdrawals 

1915 

Jan.  16 

$500.00 

Feb.  19 

700.00 

. 

Mar.  1 

i  25.00 

Mar.  8 

60.00 

June  10 

125.00 

July  19 

60.00 

Aug.  5 

200.00 

Oct.  19 

• 

145.00 

Nov.  20 

125.00 

240.  Postal  Savings  Banks.  The  United  States  Government 
has  provided  a  savings  bank  system  operated  in  conjunction  with 
the  postal  service,  whereby  savings  may  be  deposited  at  interest 
with  the  security  of  the  United  States  Government. 

Deposits.  Any  person  ten  years  of  age  or  over  may  become  a 
depositor.  Sums  less  than  1 1.00  cannot  be  deposited.  No  person 
can  deposit  more  than  $100.00  in  any  one  calendar  month,  nor 
have  a  balance  at  any  time  of  more  than  $500.00,  exclusive  of 
interest.  Depositors  receive  a  postal  savings  certificate  for  the 
amount  of  each  deposit.  Interest  is  allowed  on  these  certificates 
at  the  rate  of  two  per  cent  for  each  full  year  that  the  money  re- 
mains on  deposit,  beginning  with  the  first  day  of  the  month  following 
the  one  in  which  it  was  deposited. 

Withdrawals.  Money  may  be  withdrawn  by  surrendering  to 
the  officer  where  the  deposit  was  made  the  savings  certificates 
covering  the  desired  amount. 

Bonds.  Under  certain  conditions  a  depositor  may  surrender 
certificates  in  amounts  of  $  20.00  or  any  multiple  of  $20.00,  up  to 
and  including  $  500.00  and  receive  in  return  government  bonds 
bearing  interest  at  2 J  %  per  year.  These  postal  savings  bonds 
may  be  held  in  addition  to  the  $  500.00  deposit  allowed  to  one 
depositor. 


SAVINGS  BANKS  '  287 

Written  Work 

1.  How  much  interest  would  a  man  receive  if  he  deposited 
815.00  in  a  postal  savings  bank  on  March  1,  1915,  and  withdrew 
it  three  months  later  ? 

2.  How  much  interest  would  he  receive  if  he  withdrew  the 
money  on  March  11,  1916  ? 

3.  A  man  made  the  following  deposits  in  a  postal  savings  bank: 

May  20,  1915  115.00 

June  17,  1915  6.00 

August  11,  1915  26.00 

October  29,  1915  17.00 

When  would  he  be  entitled  to  the  full  year's  interest  on  each  of 
his  deposits,  and  how  much  interest  would  he  receive  all  together  ? 


CHAPTER   XXVIII 

CONTRACT  PURCHASES   AND  INSTALLMENT  PAYMENTS 

Real  estate  and  other  forms  of  property  are  often  purchased  and 
sold  on  contracts.  Such  contracts  usually  specify  that  the  pur- 
chaser shall  make  periodic  payments  of  a  stated  sum  in  payment 
of  accrued  interest  and  principal.  The  contract  may  permit  the 
purchaser  to  pay,  if  he  desires,  a  larger  sum  than  that  specified  by 
the  contract. 

241.  Applying  the  Payment  to  reduce  the  Principal.  Contracts 
vary  widely  in  the  provisions  for  reducing  the  principal.  The 
following  typical  cases  will  illustrate  : 

a.  C  borrows  f  1000.00  from  D  on  May  1,  1915  at  6  %,  under  a 
contract  to  pay  i  25.00  on  the  first  day  of  each  month.  Each 
payment  of  f  25.00  to  be  applied  as  follows  : 

1.  To  pay  the  interest  on  the  unpaid  principal  for  the  preceding 
month ; 

2.  The  balance  of  the  payment  to  be  applied  immediately  to  the 
reduction  of  the  principal. 

A  record  of  the  payments  might  be  kept  in  the  following 
manner : 


Date 

Payment 

Accrued 
Interest 

Balance  of  Pay- 
ment TO  Apply 
ON  Principal 

Principal 

May  1,  1915 

$1000 

00 

June  1,  1915 

$25 

00 

-15 

00 

$20 

00 

980 

00 

July  1,  1915 

25 

00 

4 

90 

20 

10 

959 

90 

Aug.  1,  1915 

25 

00 

4 

80 

20 

20 

939 

70 

b.  On  September  1,  1915,  M  sells  a  house  to  N  for  $6400.00. 
N  pays  cash  $2500.00  and  signs  a  contract  agreeing  to  pay  in- 

288 


CONTRACT  PURCHASES 


289 


stallments  of  §35.00  monthly,  with  the  privilege  of  paying  larger 
amounts.     Each  payment  is  to  be  applied  as  follows : 

At  the  expiration  of  every  quarter  (three  months)  the  total 
accrued  interest  at  6  %  is  to  be  deducted  from  the  total  payments, 
and  the  balance  applied  to  the  reduction  of  the  principal. 

A  record  of  the  payments  might  be  kept  in  the  following 
manner : 


Date 

Payments 

Total 
Payments 

ACCKUED 

Interest 

Balance  to 
Apply  on 
Principal 

Principal 

Sept.  1,  1915 

$3900 

00 

Oct.  1,  1915 

$35 

00 

Nov.  2,  1915 

45 

00 

Dec.  1,  1915 

35 

00 

$115 

00 

$58 

50 

$.56 

50 

3843 

50 

Jan.  2,  1916 

60 

00 

Feb.  1,  1916 

35 

00 

March  1,  1916 

40 

00 

135 

00 

57 

65 

77 

35 

3766 

15 

Written  Work 

1.  Check  the  items  in  the  above  form. 

2.  On  May  1, 1917,  G.  A.  Sanders  sold  a  house  and  lot  to  A.  R. 

Grain;  purchase  price,  84850.00.     Mr.  Grain  paid  12900.00  cash 
and  gave  the  following  note  for  the  balance. 

$  1950.00  Bartlett,  Iowa,  May  1,  1917. 

For  Value  Received,  I  promise  to  pay  to  the  order  of  G.  A.  Sanders,  the 
sum  of  Nineteen  Hundred  and  Fifty  Dollars,  with  interest  thereon  at  the  rate 
of  six  per  cent  per  annum,  principal  and  interest  payable  in  monthly  install- 
ments in  the  sum  of  twenty-five  dollars  or  more,  each,  the  first  of  which  is  due 
on  June  1,  1917,  and  one  on  the  first  day  of  each  and  every  month  thereafter 
until  said  principal  sum  of  Nineteen  Hundred  and  Fifty  Dollars  and  interest 
thereon  are  fully  paid. 

Each  and  every  of  said  installments  is  to  be  applied  as  follows: 
1st.     In  payment  of  accrued  interest  on  said  sum  of  $1950.00  or  on  the  un- 
paid portion  thereof. 

2d.     In  monthly  reduction  of  said  principal  sum  of  $  1950.00. 

A.  R.  Grain. 


)0                              CONTRACT  PURCHASES 

Payments  were  made 

as  follows : 

June  2,  1917 

125.00 

January  2,  1918 

$40.00 

July  1,  1917 

25.00 

February  2,  1918 

25.00 

August  1,  1917 

30.00 

March  2,  1918 

32.50 

September  1,  1917 

25.00 

April  1,  1918 

25.00 

October  1,  1917 

27.50 

May  1,  1918 

45.00 

November  1,  1917 

35.00 

June  1,  1918 

25.00 

December  1,  1917 

25.00 

Notice  that  some  payments  are  made  on  the  second  day  of  the 
month,  due  to  the  fact  that  the  first  day  of  the  month  was  either 
a  Sunday  or  a  holiday. 

Prepare  a  statement  similar  to  the  illustration  on  page  288, 
showing  a  record  of  the  payments  made. 

3.  Assume  that  the  contract  between  Mr.  Sanders  and  Mr. 
Grain  called  for  a  monthly  payment  of  125.00  or  more,  and  that 
the  principal  was  to  be  decreased  semi-annually  by  the  balance  of 
the  payments  remaining  after  paying  all  accrued  interest.  Pre- 
pare a  statement  similar  to  the  illustration  on  page  289,  showing  a 
record  of  the  payments  made. 

4.  Which  of  the  two  propositions  is  better  for  the  purchaser  ? 
Explain, 


CHAPTER   XXIX 

DISCOUNTING  NOTES  AND   OTHER  COMMERCIAL  PAPER 

242.  Borrowing  from  a  Bank.  Banks  prefer  to  have  the  bor- 
rower pay  the  interest  in  advance.  The  interest  may  be  paid  in 
cash,  or  the  bank  may  subtract  it  from  the  face  of  the  note,  giv- 
ing the  borrower  the  difference,  which  is  called  the  proceeds. 

If  you  gave  a  bank  the  following  note : 

$100,00  Chicago,  III.,  March,  2,  1915. 

Ninety  days  after  date,  I  promise  to  pay  to  the  order  of  the  Bowen  National 

Bank  One  Hundred  Dollars. 

Your  Signature 

the  bank  would  deduct  ninety  days'  interest,  il.50,  and  you  would 
receive  the  proceeds,  198.50. 

Note.  There  is  no  promise  to  pay  interest,  because  the  interest  is  prepaid. 
Banks  charge  any  rate  they  choose,  within  the  limits  set  by  the  state  law.  In 
this  text,  when  no  rate  is  mentioned  use  6  %. 

The  above  illustration  shows  the  method  of  discounting  a  note. 

243.  Terms  Used  in  Bank  Discount.  The  following  terms  are 
frequently  used,  and  you  should  become  familiar  with  them : 

Maturity  means  the  date  on  which  the  note  is  due. 

The  value  of  the  note  is  the  amount  due  at  maturity. 

If  the  note  draws  interest,  the  value  is  the  sum  of  the  principal 
and  the  interest.     Otherwise,  the  value  is  the  face  of  the  note. 

The  discount  period  is  the  exact  number  of  days  between  the 
date  of  discounting  the  paper  and  its  maturity. 

The  bank  discount  is  the  simple  interest  on  the  value  for  the 
discount  period. 

The  difference  between  the  value  and  the  bank  discount  is  called 
the  proceeds. 

291 


292 


DISCOUNTING  NOTES 


Oral  Work 
In  the  illustration  on  the  previous  page  what  is : 

The  maturity?  The  discount  period? 

The  proceeds? 


The  value  ? 

The  bank  discount? 


244.    To  find  the  bank  discount  and  the  proceeds. 

To  compute  the  hank  discount,  compute  the  simj^le  interest  on  the  value 
of  the  note  for  the  discount  period. 

To  find  the  proceeds,  subtract  the  hanlc  discount  from  the  value  of  the 
note. 

Written  Work 

How  much  would  you  receive  from  the  bank  if  you  discounted 
the  following  notes  ? 

1.  A  note  for  1^500,  without  interest,  due  in  30  days,  discounted 
at  6  %. 

2.  A  note  for  $  725,  without  interest,  due  in  two  months,  dis- 
counted at  6  %. 

3.  A  note  for  ^85.50,  without  interest,  due  in  90  days,  dis- 
counted at  7  %. 

4.  The  following  blank  shows  the  value  of  several  notes  and 
the  periods  for  which  they  were  discounted.  Compute  the  bank 
discount  at  6  %,  and  fiud  the  proceeds. 


Note 

Value 

Due  In 

$87.00 

$265.00 

$962.50 

$1000.00 

$275.00 

$765.00 

$35.00 

30  days 

Bank  discount 
Proceeds 

.44 

86.56 

60  days 

Bank  discount 
Proceeds 

80  days 

Bank  discount 
f^roceeds 

90  days 

Bank  discount 
Proceeds 

120  days 

Bank  discount 
Proceeds 

DISCOUNTING  NOTES  293 

245.  Discounting  the  Paper  of  Other  Persons.  If  you  have  a 
note  signed  by  some  person  of  good  financial  standing,  you  can 
borrow  money  on  it  by  discounting  it  in  the  same  way  that  you 
would  discount  a  note  made  by  yourself. 

Suppose  John  Doe  had  given  you  the  following  note  : 

$  500.00  Chicago,  III.,  January  1&,  1915. 

Ninety  days  after  date  I  promise  to  pay  to  the  order  of  Your  Name,  Five 

Hundred  Dollars.- 

John  Doe. 

By  the  following  indorsement, 

Pay  to  the  order  of 
The  First  National  Bank 
(Your  Name) 

you  transfer  the  note  to  the  bank.  Moreover  you  promise  to  pay 
the  bank  |500  on  April  16,  in  case  Doe  fails  to  do  so.  The  bank 
will  loan  you  i  500  minus  the  discount. 

When  you  discounted  your  own  note  (in  the  exercise  just 
given),  you  did  so  on  the  same  day  that  the  note  was  made.  The 
discount  period  and  the  time  of  the  note  were  therefore  the  same. 
But  you  may  keep  the  notes  of  other  people  some  time  before 
discounting  them.  The  bank  will  charge  you  interest  from  the 
day  you  discount  the  note  until  it  is  due. 

Thus,  if  you  did  not  discount  the  above  note  until  March  6, 
the  bank  would  charge  you  interest  for  the  number  of  days  from 
March  6  to  April  16,  the  date  of  maturity.  How  many  days  in 
this  discount  period  ? 

What  would  be  the  discount  period  if  you  discounted  the  note 
January  23  ?  February  16  ?  March  20  ? 

246.  To  find  the  discount  period. 

Find  the  maturity  of  the  note. 

Find  the  exact  number  of  days  between  the  date  of  discount  and 
the  date  of  maturity, 

247.  To  find  the  maturity.  Notes  due  a  certain  number  of 
months  after  date  fall  due  on  the  same  day  of  the  month  as  the 
day  on  which  they  were  made,  with  the  following  exceptions  : 

Notes  made  on  the  31st,  maturing  after  a  specified  number  of 


294  DISCOUNTING  NOTES 

months,  falling  due  in  a  month  having  only  30  days,  mature  on 
the  30th. 

Notes  made  on  the  28th,  29th,  30th,  or  31st,  maturing  after  a 
specified  number  of  months,  falling  due  in  February,  mature  on 
the  last  day  of  February. 

Examples. 

Note  Made  Dttb  in  Maturity 

Jan.  16,  1915  2  months  March  16,  1915 

July  31,  1915  2  months  September  30,  1915 

Dec.  31,  1915  2  months  February  29,  1916 

Notes  due  a  certain  number  of  days  after  date,  mature  after  the 
exact  number  of  days  has  elapsed. 

Examples. 

Note  Made  Due  in  Maturity 

1915 
a.      Feb.  16  30  days  March  18 

Since  February  has  only  28  days,   the   30  days  of  the 
note  will  be  divided  as  follows  : 

12  February  days  (after  the  16th) 
18  March  days 

h.      March  18  30  days  April  17 

March  has  31  days;  13  left  after  the  18th  ;  the  remain- 
ing 17  of  the  30  days  must  be  in  April. 

c,      April  17  30  days  May  17 

April  has  30  days;  13  left  after  the  17th  ;  the  remaining 
17  of  the  30  days  will  be  in  May. 
From  these  examples,  the  following  should  be  clear. 

To  find  the  maturity. 

Change  the  days  to  months ;  (30  days  =  1  month}. 

Assume  that  the  note  will  mature  on  the  same  day  of  some  follow- 
ing month. 

Correct  this  result  hy  subtracting  1  day  for  each  month  of  31  days 
through  which  the  note  runs  ;  and  hy  adding  2  days  if  the  note  rmis 
through  February.     (^In  case  of  leap  year^  add  1  day.} 


DISCOUNTING  NOTES 


295 


The  following  table  provides  a  convenient  method  for  indicating 
the  months  for  which  corrections  are  to  be  made. 


Month 

'     Number  ( 

)F  Month 

Days 

COKREOTION 

January 

1 

13 

31 

_    ^ 

February 

2 

14 

28 

+  2  (or  +  1) 

March 

3 

15 

31 

—  1 

April 

4 

16 

30 

May 

5 

17 

31 

—  1 

June 

6 

18 

30 

July 

7 

19 

31 

—  1 

August 

8 

20 

31 

—  1 

September 

9 

21 

30 

October 

10 

22 

31 

_  1 

November 

11 

23 

30 

December 

12 

24 

31 

—  1 

Examples.     1.    Find  the  maturity  of  a  note  dated  May  16,  1915, 
due  in  4  months. 

Solution.     May  is  the  fifth  month.     Add  4  months.     The  note  will  be  due 
in  the  ninth  month,  which  by  the  table  is  September. 
Maturity,  September  16. 

2.  Find  the  maturity  of  a  note  of  the  same  date,  due  in  120 
days. 

Solution.     Call  120  days  4  months. 

May  is  the  fifth  month.     The  note  is  due  in  the  ninth  month,  shown  by  the 
table  to  be  September. 

Call  the  maturity  September  16.     Correct  as  follows: 
Note  runs  through  May  Subtract  1  day 

Note  runs  through  July  Subtract  1  day 

Note  runs  through  August  Subtract  1  day 

Total  3  days 

Therefore  the  maturity  is  September  13. 

3.  Find  the  maturity  of  a  note  dated  December  19,  1914,  due 

in  150  days. 

Solution.     Call  150  days  5  months. 

December  is  the  twelfth  month.     The  note  is  due  in  the  seventeenth  months 
which,  by  the  table,  is  May. 
Call  the  maturity  May  19,  1915. 


296 

Correct  as  follows : 


DISCOUNTING  NOTES 


December  —  1 

January  —  1 

February  +  2 

March  —  1 

April  (has  30  da.) 

Note  does  not  run  through  May.  

Total  -  1 
Maturity,  May  18,  1915. 

4.    Find  the  maturity  of  a  note  dated  June  16,  1915,  due  in  70 
days. 

Solution.     Call  70  days  2  months,  10  days. 

June  16  plus  two  months  is  August  16;  plus  10  days  is  August  26. 

To  correct : 

For  June 

For  July  -  1 

Total  -  1 

Maturity,  August  25,  1915. 


Written  Work 
Enter  the  maturity  of  each  note  in  the  proper  column: 


Note  Dated 


Sept.  23,  1915 
Oct.  9,  1915 
Mayl,  1915 
July  20,  1915 
Dec.  15,  1915 
Feb.  9,  1915 


Due  in 
1  Month 


Due  in 
80  Days 


Due  in 
2  Months 


Due  in 
60  Days 


Due  in 
150  Days 


Due  in 
45  Days 


248.    To  find  the  discount  period.      Compute  the  actual  number 
of  days  between  the  date  of  discount  and  the  date  of  maturity. 

Illustration.     A  note,  dated  July  17,  due  in  4  months,  was  dis- 
counted on  August  5.     What  was  the  discount  period  ? 

Solution.    Four  months  from  July  17  is  November  17,  the  date  of  maturity. 
The  discount  period,  therefore,  extends  from  August  5,  the   date  of  dis- 
count, to  November  17,  the  date  of  maturity. 


DISCOUNTING  NOTES 


297 


To  find  the  number  of  days  between  August  5  and  November  17 : 

31  total  number  of  days  in  August 

5  number  of  August  days  expired  before  discounting 

26  number  of  August  days  in  the  discount  period 

30  number  of  September  days  in  the  discount  period 

31  number  of  October  days  in  the  discount  period 
17  number  of  November  days  in  the  discount  period 

104     total  number  of  days  in  the  discount  period 

Oral  Work 

After  studying  the  illustration,  state  a  method  for  finding  the 
number  of  days  in  the  discount  period. 

Written  Work 

1.    On  a  form  ruled  like  the  following,  enter  the  date  of  ma- 
turity on  the  upper  line,  and  the  discount  period  on  the  lower  line. 
The  notes  dated  February  12  were  discounted  April  8. 
The  notes  dated  February  17  were  discounted  March  2. 
The  notes  dated  March  23  were  discounted  April  29. 
The  notes  dated  March  17  were  discounted  April  15. 
The  notes  dated  March  30  were  discounted  May  20. 


Dates  Notes 
WERE  Made 

Time 

60  Days 

75  Days 

100  Days 

120  Days 

6  Months 

Feb.  12,  1915 

Feb.  17,  1915 

Mar.  23,  1915 

Mar.  17,  1915 

Mar.  30,  1915 

2.    Complete  a  table  ruled  like  the  following  model.     Enter  the 
date  of   maturity  on  the  first   line,  the  discount    period  on  the 


298 


DISCOUNTING  NOTES 


second  line,  the  discount  on  the  third  line,  the  proceeds  on  the 
fourth  line,  as  illustrated  by  the  first  problem  in  the  table. 


Date  of  Papkr 
AND  Face 

Time,  90  Days 

Time,  3  Months 

Time,  120  Days 

Time,  6  MjOnths 

Discounted 
April  13 

Discounted 
Ai>ril  11 

Discounted 
April  28 

Discounted 

May  20 

Jan.  16,  1915 

1300 

April  16 

3  days 

1.15 

$299.85 

Jan.  30,  1915 

1285 

Feb.  19,  1915 

$126 

249.  Discounting  Interest-bearing  Notes.  If  you  had  in  your 
possession  the  following  note  and  wished  to  discount  it,  you  would 
first  add  90  days'  interest  (11.50)  to  the  face  of  the  note  to  deter- 
mine its  value  at  maturity.  This  note  is  really  Roe's  promise  to 
pay  you  $101.50  at  maturity,  and  the  bank  will  give  you  as  much 
for  it  as  for  a  note  for  $101.50  without  interest. 


'^  rf  /oo~ 


-^'^^W^^^^  ^gg^ii'^^ii^ 


*^V^^^-vr7^v?-;      Ua.--yt.£^:.^Z./i^ 


J^/'y./>?-Y^^-'/yy  (  '^^^^yt^^.^^t^y^^.  ) 


■_y^(^^x^^^^^^^/^^^^^<^y^ 


K.J-^^c^-^^^^y^r^:^^^.^.^^^  ^ 


2)x^//a 


yyouaU 


y//"  .t^yi^^  ^^7^^^^^,  -^c^^^^^^'-n.i'^iyt^d^  ^    ^/o. 


9^^^^^^-  9^ 


'='«>««»»=**°**«««'«»««»«''*«'««*»'»«*^^ 


DISCOUNTING  NOTES 


299 


When  discounting  interest-bearing  paper,  compute  the  interest 
for  the  full  time  the  note  is  to  run,  and  add  this  interest  to  the  face, 
to  determine  the  value  at  maturity.  Find  the  discount  on  this 
value.  Subtract  the  discount  from  the  value  to  determine  the 
proceeds. 

Written  Work 

Complete  a  table  ruled  like  the  following  model,  entering  the 
facts  as  illustrated  in  the  first  problem. 
All  notes  discounted  at  6  <5^. 


Time,  90  Days 

Time,  4  Months 

Time,  6  Months 

Without 
Int. 

With 
Int.  6% 

Without 
Int. 

With 
Int. 6  % 

Without 
Int. 

With 
Int.  5% 

Principal, 

$500.00 
Date  of  Paper, 

June  3,  1915 
Date  of  Discount 

Aug.  21,  1915 

Maturity 
Interest 
Value 
Dis.  Period 
Bank  Dis. 
Proceeds 

Sept.   1 

$500.00 
11  days 

$       .92 
$  499.08 

Sept.  1 
$     7.50 
$507.50 
11  days 
$       .93 
$506.57 

Principal, 

$1250.00 
Date  of  Paper, 

Aug.  6,  1915 
Date  of  Discount 

Sept.  18, 1915 

Maturity 
Interest 
Value 
Dis.  Period 
Bank  Dis. 
Proceeds 

Principal, 

$47.96 
Date  of  Paper, 

July  16,  1915 
Date  of  Discount 

Aug.  27,  1915 

Maturity 
Interest 
Value 
Dis.  Period 
Bank  Dis. 
Proceeds 

Principal, 

$55.00 
Date  of  Paper, 

Aug.  14, 1915 
Date  of  Discount 

Oct.  5,  1915 

Maturity 
Interest 
Value 
Dis.  Period 
Bank  Dis. 
Proceeds 

300  DISCOUNTING  NOTES 

250.  Discounting  Acceptances.  Time  drafts  were  discussed  in 
Chapter  XIX.  An  accepted  draft  is  a  written  promise  of  the 
acceptor  to  pay  money  at  a  definite  date,  and  accepted  drafts  may 
be  discounted,  just  as  notes  may  be  discounted.  In  case  the  person 
who  has  accepted  the  draft  does  not  pay  it  when  due,  the  person 
who  discounted  it  will  be  required  to  pay  it. 

The  following  draft  drawn  by  you  on  John  Doe  and  accepted 
by  him  is  just  as  truly  his  promise  to  pay  $,500.00  at  a  given  date, 
as  a  promissory  note  signed  by  him  would  be. 


-<^oo~ jS;,^^^^  ^(l^^^^yr^^.  ^  ,^ ^^J^SL. 


C^^icyt^/.  .^/<:t^/^^ 


t^g^^ 


g^^^ 


r^:J.^..^^..^.  ^-^ 


.AP  ^.^    ^^ 


This  draft  could  be  discounted  in  exactly  the  same  manner  as  a 
note  dated  January  6,  payable  30  days  after  date. 

If  the  draft  were  drawn  payable  30  days  after  sight,  instead  of 
after  date,  the  bank  discount  would  be  different  because  the  date 
of  maturity  would  be  different. 


i:^^3i£sS-::^6iiifc2i2^fe2i2^1_^^^^ 


^ 


v^^ 


C/yO' [Lr^.t^    ^2t»^ 


DISCOUNTING  NOTES  301 

Written  Work 

1.  What  is  the  date  of  maturity  of  the  draft  on  page  300  pay- 
able 30  days  after  date? 

2.  What  is  the  date  of  maturity  of  the  draft  on  page  300  pay- 
able 30  days  after  sight? 

3.  What  is  the  discount  period  of  each  draft  if  discounted  on 
Jan.  14? 

4.  Find  the  bank  discount  and  the  proceeds  of  each  draft. 

Review 

Write  the  notes  and  drafts  called  for  in  the  following.  Show 
all  acceptances  and  indorsements. 

On  October  3,  you  received  from  B.  A.  Anderson,  of  Batavia, 
New  York,  a  note  dated  October  1,  due  in  two  months,  for  $135.00, 
without  interest. 

On  August  28,  you  sold  to  N.  M.  Davis,  of  Toledo,  Ohio,  an  in- 
voice of  goods  amounting  to  $84.00;  terms  1/10;  N/30.  This 
invoice  was  due  September  27,  but  Mr.  Davis  was  unable  to  pay 
it.  He  agreed,  however,  to  accept  a  thirty-day  draft  for  the  amount. 
You  drew  the  draft  on  September  30,  payable  thirty  days  after 
date,  and  sent  it  to  him  for  acceptance.  He  accepted  it  and  re- 
turned it  to  you. 

On  October  5,  you  sold  a  bill  of  goods  amounting  to  $68.00  to 
J.  D.  Robinson,  of  Burlington,  Iowa.  Terms,  30  day  draft  less  1  %. 
On  October  5,  you  drew  a  draft  on  him,  payable  30  days  after 
sight ;  he  accepted  the  draft  on  October  7. 

On  July  10,  you  received  from  J.  F.  Cook  of  Lime  Springs, 
Iowa,  a  note  made  by  him  on  July  8,  in  your  favor,  for  $500.00, 
due  six  months  after  date,  with  interest  at  6  %. 

On  June  4,  you  received  a  note  for  $600.00  from  A.  B.  Hicks 
of  Chicago.  The  note  was  drawn  on  April  16,  by  D.  F.  Fairchild 
of  Omaha,  Nebraska,  in  favor  of  Hicks,  payable  nine  months 
after  date,  without  interest,  and  was  transferred  to  you  by  full 
indorsement. 

On  October  15,  you  took  these  notes  and  drafts  to  the  Dairy 
State    Bank   to   discount.     The   bank's    discount   rate   was    6%. 


302  DISCOUNTING  NOTES 

Finding  that  the  proceeds  would  not  be  sufficient  to  meet  your 
needs,  you  gave  the  bank  your  own  note,  dated  October  15,  due 
in  20  days,  for  1250.00,  without  interest. 

1.  Find  the  proceeds  of  each  of  the  papers  discounted. 

Your  balance  at  the  bank  before  discounting  this  paper  was 
$167.25.  You  deposited  the  proceeds  of  the  discounted  paper. 
What  was  your  balance  after  discounting  the  paper? 

2.  On  October  25,  the  bank  wished  to  increase  its  deposit  with 
its  correspondent  bank  at  Chicago.  It  therefore  rediscounted  the 
notes  and  drafts  received  from  you.  How  much  did  the  bank 
receive  for  the  paper,  when  discounted  on  October  25  at  6  %  ? 

3.  Marshall  owed  Daniels  $485.90;  on  September  23  he  gave 
Daniels  the  following  note,  properly  indorsed. 

1450.00  Brainerd,  Iowa,  September  3,  1915. 

Sixty  days  after  date,  I  promise  to  pay  to  the  order  of  J.  F.  Marshall,  Four 
Hundred  and  Fifty  Dollars. 

Value  received 

Without  interest.  F.  S.  Crosby. 

How  much  did  Marshall  owe  Daniels  after  transferring  the 
note? 


BUSINESS  EXPENSES 


CHAPTER   XXX 


WAGES  AND  PAY  ROLLS 

There  are  several  wage  systems  in  use,  each  of  which  is  designed 
to  encourage  employees  to  produce  as  much  as  possible.  Several 
of  the  most  common  systems  will  be  discussed  in  this  chapter. 

251.  The  Day  or  Hour  Rate.  This  system  is  the  one  generally 
used,  because  it  is  the  simplest.  When  the  day  or  hour  rate  is 
used,  the  employee's  wage  depends  upon  the  time  he  has  labored. 
Work  done  overtime  or  on  holidays  is  usually  paid  for  at  one  and 
one  half  times  the  regular  rate.  In  many  factories  time  clocks 
are  installed.  As  each  employee  begins  work,  he  registers  the 
time  on  his  card  ;  when  he  stops  work,  he  again  registers  the 
time.  At  the  end  of  the  week,  each  employee's  card  shows  his 
actual  hours  of  labor.  A  pay  roll  is  prepared  showing  the  total 
number  of  hours  each  employee  has  worked,  his  hourly  rate,  and 
his  total  wage. 

Written  Work 

Supply  the  missing  facts  in  the  following  pay  roll. 


No 

Name 

Hours  worked  per  day 

Time 

Overrime 

Total  Wa<ea 
Earned 

Mone> 

Wafet 

M 

T 

w 

T 

F 

S 

Hr». 

Rate 

Amouni 

Hr.. 

Amount 

Advanced 

Due 

.  y 

,sCt.<,(t^^?>h42j!g^ 

(7 

f 

<7 

., 

a 

<"■? 

,^n 

/>5 

(-o 

^ 

/'.O 

/~S' 

/.n 

a. 

1-7 

I-? 

/•  f 

fT 

'f 

i7 

I'i'f- 

Pf 

/J 

/•? 

•  ■5- 

S 

/f) 

/'r 

■?"? 

/  "y 

t*} 

f 

•? 

? 

/^ 

,? 

(7 

ft 

a 

r7 

? 

Oq 

? 

? 

7 

JT 

O 

(7 

/|0 

'0 

// 

n 

9 

■'■■ 

? 

9 

? 

<? 

/ 

a.o 

1' 

£ 

; 

? 

cr 

<7 

/7 

(f 

9 

..r 

^ 

7 

? 

-  7 

,^^^.<^^J^.J^^ 

. 

? 

.. 

9 

? 

^ 

•S 

.  s 

<^^^^^rL,.^^ 

. 

^ 

f 

f 

'? 

7 

? 

? 

-  <? 

;. 

,oK 

,fi 

? 

A'T 

9 

? 

p 

? 

/ 

JS 

? 

, 

In  this  factory  a  full  day  is  9  hours.  Any  over  hours  are  paid 
for  at  IJ  times  the  regular  rate.  Thus,  Calkins  gets  1^  times 
regular  pay  for  the  overtime  on  Thursday  and  Friday,  even 
though  he  did  not  work  full  time  on  Monday. 

303 


304  WAGES  AND  PAY  ROLLS 

2.  Rule  a  pay  roll  similar  to  the  model,  and  enter  the  following 
data,  finding  the  amount  of  wages  due  each  employee. 

The  superintendent  supplies  the  cashier  with  the  following  list 
of  the  employees,  together  with  their  numbers,  and  the  hourly 
wage  rate  paid  each.  A  full  day  in  this  factory  is  9  hours,  and 
overtime  is  paid  for  at  1^  times  the  regular  rate. 

No.  Employee's  Name  Hourly  Kate 

1.  Fred  Smith  |.35 

2.  Frank  Bailey  .32 

3.  Charles  Hanchett  .30 

4.  Harry  Davis  .36 

5.  Carl  Bell  .38 

6.  Lewis  Clark  .40 

7.  Arthur  Helms  .29 

8.  Tony  Martin  .31 

9.  Henry  Dickinson  .26 
10.  Nathan  Wright  .37 

During  the  week  ending  March  15,  time  tickets  were  turned  in  by 
the  foreman,  showing  the  hours  worked  by  each  employee. 

Monday:  1,  9  (Workman  No.  1,  9  hours);  2,  11 ;  3,  8 ;  4, 
11 ;   5,  8  ;   6,  10  ;   7,  9  ;   8,  12  ;   9,  9  ;   10,  8. 

Tuesday :   1,  9 ;  2,  11 ;  3,  9 ;  4,  9 ;  5,  10 ;  6,  9 ;  7,  9 ;  8,  9 ;  10,  9. 

Wednesday:   1,  10;   2,  12;   3,  11 ;  4,  12 ;  5,    9 ;  6,  11 ;   7,   8 ; 

8,  11 ;  9,  10  ;  10,  9. 

Thursday  :   1,  9 ;   2,  9  ;   3,  11 ;  4,  10  ;   6,  8  ;   6,  10 ;   7,  11 ;   8,  11 ; 

9,  12 ;  10,  10. 

Friday:  1,  5 ;  2,  9;  3,  11 ;  4,  10 ;  5,  9;  6,  9 ;  7,  9 ;  8,  9;  9, 
10 ;   10,  8. 

Saturday:  1,9;  2,11;  3,11;  4,10;  5,11;  6,9;  7,12;  8,9; 
9,  4  ;   10,  9. 

The  cashier  lias  already  advanced  Charles  Hanchett  §3.00; 
Carl  Bell,  12.25;  Tony  Martin,  13.75  ;  and  Nathan  Wright,  $5.00. 

252.  Piecework  Wage  System.  The  piecework  wage  system 
is  based  on  the  theory  that  if  the  employee  is  paid  for  the  actual 
amount  of  work  he  accomplishes,  he  will  produce  more  in  a  day 
than  if  he  is  paid  a  straight  hour  or  day  wage. 


WAGES*  AND  PAY  ROLLS 


305 


The  pay  roll  prepared  under  a  piecework  system  is  similar  to 
that  prepared  under  the  hourly  rate  system,  with  the  exception 
that  overtime  is  usually  paid  for  at  the  same  rate  that  regular  time 
receives,  and  the  basis  of  the  wage  is  the  number  of  pieces  pro- 
duced and  not  the  number  of  hours  employed. 

Written  Work 
Find  the  missing  facts  in  the  following  pay  roll. 

Piecework  Pay  Roll  for  Week  Ending  June  8,  19 — 


No. 

Name 

Opera- 
tion 

Number  Produced 

Total 

Rate 

Earned 

Ad- 

Due 

Number 

M. 

T. 

W. 

T. 

F. 

S. 

1 

John  Sanford 

264 

16 

14 

17 

13 

15 

18 

93 

.14 

13 

02 

2 

11 

02 

2 

Irving  Banner 

178 

23 

26 

22 

27 

24 

25 

? 

.12 

? 

? 

3 

Byron  Shepley 

861 

37 

33 

34 

39 

36 

30 

9 

.08 

? 

? 

4 

Edward  Magee 

422 

28 

27 

29 

28 

26    27 

? 

.05 

? 

3 

25 

? 

5 

Percival  Conrad 

267 

42 

45 

41 

39 

43 

20 

? 

.07 

? 

? 

6 

Ernest  Anderson 

207 

24 

26 

20 

23 

30 

27 

9 

.09 

? 

2 

60 

? 

253.  The  Differential  Rate.  The  differential  rate  is  a  modifica- 
tion of  the  piecework  system.  A  standard  day's  work  is  deter- 
mined, and  each  employee  is  expected  to  produce  this  standard 
amount  of  work.  If  he  produces  the  standard,  he  receives  a  cer- 
tain rate  per  piece.  If  he  produces  less  than  the  standard,  he 
receives  a  lower  rate  per  piece.  If  he  produces  more  than  the 
standard,  he  receives  a  higher  rate  per  piece. 

This  system  is  based  on  the  theory  that  the  expense  of  heat, 
light,  rent,  power,  etc.,  remains  about  the  same,  whether  the 
employees  produce  a  small  amount  of  product,  or  a  large  amount. 
By  increasing  the  amount  of  output,  these  expenses  are  distributed 
over  a  larger  quantity  of  manufactured  goods,  and  the  cost  of 
making  each  article  is  thereby  decreased.  The  saving  effected 
by  increasing  the  output  is  divided  between  the  owner  of  the 
factory  and  the  workmen  who,  by  their  skill  or  industry,  increase 
the  output.  On  the  other  hand,  the  employees  who,  by  producing 
a  small  quantity,  tend  to  increase  the  cost  per  article  are  paid 
at  a  lower  rate. 


306  WAGES  AND  PAY  ROLLS 

Example.  A  manufacturer  learned  by  experience  that  the 
average  workman  in  his  factory  could  produce  ten  articles  per 
day,  and  that  25  cents  per  article  could  be  paid  for  the  work. 
He  then  adopted  a  differential  rate,  as  follows  : 

NuMBEE  OF  Pieces  Pkoduokd  Kate  pee  Pisos 

7  $.20 

8  .21 

9  .23 
10,  Standard  .25 

11  .26 

12  .27 

Jones  produced  the  standard  quantity  on  Wednesday,  and  re- 
ceived 10  X  1.25  =  12.50. 

Smith  produced  8  pieces,  and  received  8  x  f  .21  =  il.68. 
Brown  produced  12  pieces,  and  received  12  x  $.27  =  13.24. 


Written  Work 

iwing  differential  rate  applies  in  a 

certair 

ruMBEE  OF  Pieces 

Rate 

10 

1.12 

11 

.13 

12 

.14 

13 

.15 

14 

.17 

15 

.19 

16 

.21 

17 

.22 

18,  Standard 

.24 

19 

.-25 

20 

.27 

21 

.29 

22 

.31 

23 

.33 

24 

.33^ 

25 

.34 

WAGES  AND  PAY  ROLLS 


307 


The  production  sheet  for  the  week  ending  September  17,  19 — 
was  as  follows  : 


No. 

Name 

Daily  PaorucTiON 

M. 

T. 

w. 

T. 

F. 

s. 

1 

Edward  Dye 

17 

19 

18 

16 

19 

18 

2 

Frank  Bartlett 

14 

15 

14 

16 

15 

14 

3 

Arthur  Bassett 

19 

20 

19 

21 

22 

19 

4 

James  Hamilton 

22 

21 

21 

23 

20 

21 

5 

Den  Slocum 

12 

14 

13 

15 

12 

14 

6 

John  Gay  lord 

13 

16 

15 

16 

15 

17 

7 

Saui  Bayliss 

19 

20 

19 

21 

18 

17 

8 

George  Bates 

19 

22 

23 

20 

19 

18 

9 

Wm.  Osgood 

16 

14 

12 

14 

11 

16 

1.  Devise  a  pay  roll  blank  which  will  show  all  necessary  facts, 
and  enter  each  laborer's  production  and  wages.  See  how  good  a 
pay  roll  form  you  can  devise  without  asking  for  suggestions.  It 
should  be  simple  and  convenient,  and,  while  not  being  too  elabo- 
rate, it  should  give  all  necessary  information. 

2.  Find  the  average  daily  production  of  each  workman.  Pre- 
pare a  graph,  showing  the  standard  production  by  a  red  line  across 
the  sheet,  and  the  workmen's  averages  by  a  black  curve. 


Commission 

254.  Definitions.  An  agent  is  a  person  who  transacts  business 
for  another. 

The  principal  is  the  one  whose  business  is  transacted  by  the 
agent. 

Principals  often  pay  their  agents  a  commission  for  their 
services.  The  commission  is  usually  a  per  cent  of  the  money 
value  involved  in  the  transaction. 

Example.  A  wholesale  store  engaged  a  salesman,  agreeing  to 
pay  him  8  %  of  his  gross  sales  as  commission.     How  much  did 


308  WAGES  AND  PAY  ROLLS 

the  salesman  earn  if   he  sold   f  1425  worth   of   goods   during   a 
month  ? 

Solution.  $  1425       sales 

.08        rate  of  commission 
$114.00  commission 

Written  Work 

1.  A  real  estate  agent  sold  a  farm  belonging  to  Mr.  Robinson 
for  1 20,450.  The  agent  received  3  %  of  the  selling  price  as  pay- 
ment for  his  services.  How  much  did  the  agent  receive  ?  How 
niuch  did  Mr.  Robinson  receive  after  paying  his  agent  ? 

2.  A  manufacturer  engaged  Mr.  Seeley  as  a  traveling  salesman. 
Mr.  Seeley's  contract  stipulated  that  he  should  receive  7  %  of  his 
gross  sales  as  commission.  During  four  weeks,  his  sales  were  aa 
follows:      1576.25;     $498.49;     !^3T6.45;     1723.50. 

What  was  his  commission  each  week  ? 

3.  Mr.  Brooks,  a  merchant,  engaged  an  attorney  to  collect  a 
number  of  accounts.  The  attorney  charged  for  his  services  15  % 
of  the  amounts  collected.  What  did  the  attorney  receive  for  col- 
lecting 1354.75?  What  was  the  net  amount  received  by  Mr. 
Brooks  ? 

4.  James  Hunter  bought  eggs  for  a  Chicago  produce  merchant. 
For  his  labor  in  purchasing  and  hauling  them  to  the  station,  he 
received  1|  %  of  the  cost  of  the  eggs.  On  Tuesday  he  bought 
27  cases,  of  30  dozen  each,  paying  29  cents  per  dozen  for  them. 
How  much  did  Hunter  pay  for  the  eggs  ?  How  much  was  his 
commission  ?  How  much  did  the  eggs  cost  the  Chicago  merchant, 
not  including  the  freight  ? 

5.  The  salesmen  of  the  Wickman  Specialty  Company  receive 
the  following  commissions : 

On  goods  sold  in  Department  A,  9  %. 
On  goods  sold  in  Department  B,  1S%. 
On  goods  sold  in  Department  C,  12|  %. 
On  goods  sold  in  Department  D,  15%. 
The  following  table  shows  the  sales  made  by  five  men. 


WAGES  AND  PAY  ROLLS 


309 


SJILESMAJ^ 

DEPT.A 

DZPT.  B 

DEPT.C 

DFPT.  D 

C.  O.  T'lITErS 

3^4^21 

^y^A8 

j^^^  js 

A^^.2,3^ 

FL.SJ^OYC 

SZ3.7^ 

6'Zs:^o 

¥S^3^ 

S^^.giA 

Z,D.-\^tCKS 

2,8  3.^ J 

^ss.o^y 

:^^s<au 

^y^jg^ 

L.S.BASSETT 

^:i5>.ju 

s^s:3>C> 

y3>^.¥6 

u-6^/Ay 

rj^AUXTHOL  TZMAM 

J^S.8^ 

J>Ys:vy 

3ys.£/y 

¥^Z.SS 

Devise  a  form  which  will  show  the  above  data  and  enter  the 
following : 

Each  salesman's  commission  on  goods  sold  in  each  depart- 
ment. 

The  total  commissions  paid  to  each  salesman. 
The  total  commissions  paid  for  each  department. 
The  total  commissions  paid  to  all  salesmen. 
The  total  sales  in  each  department. 
The  total  sales  of  each  salesman. 
The  total  sales  in  all  departments. 

255.  Pay  Roll  Slips.  Laborers  are  sometimes  paid  by  check, 
and  sometimes  by  the  envelope  system.  When  the  latter  method 
is  used,  each  employee  receives  an  envelope  containing  the  exact 
amount  of  his  wages.  A  coin  sheet  is  prepared  from  the  pay 
roll,  showing  the  change  needed  for  each  envelope.     A  pay  roll 


No. 

Name 

Bi 

!s 

$.50 

$-25 

$.10 

$.05 

$.01 

Wages 

S  10.00 

$5.00 

S2.00 

$1.00 

/ 

Z2 

/.-/ 

z 

/ 

/ 

/ 

^ 

-? 

.9/ 

^7 

3 

/ 

/ 

/ 

/ 

O- 

?; 

<::^^yA.^.^.yi^^^. 

Z6 

:p. 

/ 

/ 

/ 

/ 

^ 

/X 

\A>^^j>.  (^k,.^,^^ 

.. 

,., 

. 

/ 

^ 

/ 

/ 

,^ 

^y^^^'^^JA'^^ 

.. 

if. 

/ 

/ 

/ 

/ 

/ 

^ 

f 

^ 

/s 

' 

/•s- 

/ 

/ 

/ 

/ 

/ 

/ 

-T           /"' 

. 

^^7 

So 

/& 

_^J 

L=^= 

-^^^ 

^ 

-^-^ 

r ,. 

-5 

/o 

Coin  Sheet 


310 


WAGES  AND  PAY  ROLLS 


slip,  designating  the  number  and  denomination  of  the  bills  and 
coins  desired,  is  then  filled  out  and  sent  to  the  bank.     When  the 

THE  FIRST  NATIONAL  BANK 


CURRENCY  FOR  PAY  ROLL 


DOLLARS 

CENTS 

$50   Bills. 

20 

/£i 

/Ac 

O    0 

la 

¥- 

2io 

OO 

5 

^ 

/o 

oo 

2 

^ 

^ 

OO 

1 

^3 

/ 

so 

Halves. 

v3 

7^ 

Quarters, 

'y 

JO 

Dimes. 

f 

v3 

/ 
/v5- 

Nickels. 

/O 

/o 

Pennies. 

/^7 

ZO 

TOTAL 

Pay  Roll  Slip 


currency  is  delivered  a  check  is  made  out  to  the  bank  for  the 
amount  of  the  pay  roll. 

Written  Work 

Rule  a  coin  sheet  and  enter  the  number  of  coins  of  each  denomi- 
nation necessary  to  pay  each  of  the  employees  in  the  pay  roll 
prepared  in  the  differential  wage  rate  problem  on  page  307. 

Make  out  a  pay  roll  slip  on  the  First  National  Bank  of  your 
city,  to  obtain  the  money  to  pay  these  employees. 


CHAPTER   XXXI 

POSTAGE,   FREIGHT,   AND   EXPRESS   RATES 

Postage 

256.  The  Rates  for  Domestic  Postage.  Domestic  mail  matter 
includes  all  matter  deposited  in  the  mails  for  delivery  to  points 
in  the  United  States  or  its  possessions,  including  Porto  Rico, 
Hawaii,  the  Philippine  Islands,  Guam,  and  the  Canal  Zone ;  with 
certain  exceptions,  it  includes  matter  sent  to  Canada,  Cuba, 
Mexico,  and  the  Republic  of  Panama.  The  domestic  rate  applies 
also  to  letters,  but  not  to  other  articles,  addressed  to  Great  Britain, 
Ireland,  Newfoundland,  and  Germany. 

CLASSES   OF   DOMESTIC   MAIL 

First  Class :      Written   matter :    Letters   and   all   mail   which   is 
sealed. 
Rate :  2  cents  for  each  ounce  or  fraction  thereof. 
Post  cards  and  postal  cards,  1  cent  each. 
Second  Class  :  Unsealed.     Newspapers  and  periodicals. 

Rates :  When  mailed  by  the  publisher,  1  cent  per 
pound.     When  mailed  by  others  than  the  pub- 
lisher  or   a   news   agent,  1   cent   for   each   four 
ounces   or   fraction    thereof,  on  each   separately 
addressed  copy. 
Third  Class  :     Circulars,  newspapers,  and  printed  matter  (except 
books)  not  admitted  to  the  second  class. 
Rates :    1    cent   for   each    two   ounces   or   fraction 
thereof.     The    limit    of    weight     of    third-class 
matter  is  four  pounds. 
Fourth  Class :  Parcel  post :  All  matter  not  embraced  in  the  first, 
second,  or  third  classes,  and  not  likely  to  injure 
the  employees  of  the  postal  service,  or  the  mails 
311 


312  POSTAGE,   FREIGHT,   AND  EXPRESS  RATES 

This  includes  merchandise,  farm  and  tactory 
products,  seeds,  books,  etc. 

Rates  :  Parcels  weighing  four  ounces  or  less,  except 
books,  seeds,  plants,  etc.,  1  cent  for  each  ounce  oi 
fraction  of  an  ounce,  regardless  of  the  distance. 

Parcels  weighing  eight  ounces  or  less  containing 
books,  seeds,  cuttings,  roots,  etc.,  1  cent  for  each 
two  ounces  or  fraction  thereof. 

Parcels  weighing  more  than  eight  ounces  contain- 
ing books,  seeds,  plants,  etc.,  parcels  of  miscella- 
neous printed  matter  weighing  more  than  four 
pounds,  and  all  other  parcels  of  fourth-class  mat- 
ter weighing  more  than  four  ounces  are  subject 
to  pound  rates,  a  fraction  of  a  pound  being  con- 
sidered a  full  pound.  The  pound  rates  vary 
with  the  distance  the  parcel  is  to  be  carried. 

257.  Units  of  Area  and  Zones.  For  the  purpose  of  determining 
the  various  pound  rates,  the  United  States  is  divided  into  "  units 
of  area,"  each  unit  being  thirty  miles  square.  Each  unit  is  the 
center  of  a  series  of  zones : 

First  Zone  :         Territory  within  a  radius  of  50  miles. 

Second  Zone  :     Territory  within  a  radius  of  150  miles  and  beyond 

1st  zone. 
Third  Zone  :       Territory  within  a  radius  of  300  miles  and  beyond 

2d  zone. 
Fourth  Zone  :     Territory  within  a  radius  of  600  miles  and  beyond 

3d  zone. 
Fifth  Zone :         Territory    within    a   radius   of    1000    miles   and 

beyond  4th  zone. 
Sixth  Zone :        Territory   within    a    radius   of    1400   miles   and 

beyond  the  5th  zone. 
Seventh  Zone :    Territory   within    a   radius   of    1800   miles   and 

beyond  the  6th  zone. 
Eighth  Zone  :     All  territory  beyond  the  7th  zone. 

258.  Size  and  Weight  of  Parcels.  No  package  can  be  sent  by 
parcel  post,  if  its  length  plus  its  girth  is  more  than  seventy-two 


POSTAGE,   FREIGHT,   AND  EXPRESS  RATES  313 

inches.  For  delivery  in  the  first  and  second  zones,  parcels  may 
weigh  not  more  than  fifty  pounds ;  for  delivery  in  other  zones, 
they  may  weigh  not  more  than  twenty  pounds. 

259.  Parcel  Post  Rates.  The  rates  of  postage  on  parcels  exceed- 
ing 4  ounces  in  weight  are  as  shown  on  the  opposite  page. 

The  local  rate  applies  to  parcels  to  be  delivered  from  the  same 
office  at  which  they  are  mailed.  The  delivery  may  be  made  at 
the  office,  by  city  carrier,  or  by  rural  free  delivery. 

Books.  Books  weighing  4  ounces  or  less  are  mailed  at  the 
third-class  rate  of  1  cent  for  each  2  ounces  or  fraction  thereof. 
Those  weighing  more  than  4  ounces  are  mailed  under  the  regular 
zone  rates. 

260.  Special  Regulations.  When  two  classes  of  mail  matter  are 
mailed  in  the  same  package,  the  higher  rate  is  charged  on  the 
entire  package.  For  example,  inclosing  a  letter  in  a  parcel  of 
merchandise  subjects  the  whole  parcel  to  the  letter  rate. 

As  a  general  rule  the  postage  on  all  mail  must  be  prepaid  in 
stamps  affixed  to  the  package.  Publishers,  however,  do  not 
always  affix  stamps  to  their  publications ;  and  the  postage  on 
third-class  matter,  mailed  in  quantities  of  not  less  than  2000 
identical  pieces,  may  be  paid  in  money. 

Postage  stamps  are  issued  in  the  following  denominations :  1, 
2,  3,  4,  5,  6,  7,  8,  9,  10,  12,  15,  20,  30,  and  50  cent,  and  1,  2,  and 
5  dollars. 

Special  Delivery.  By  affixing  a  "  special  delivery  "  stamp  (cost, 
10  cents),  or  ten  cents'  worth  of  ordinary  stamps,  in  addition  to 
the  regular  postage,  and  writing  the  words  "  Special  Delivery," 
prompt  delivery  by  special  messenger  is  obtained. 

Registry.  The  registry  system  provides  greater  security  for 
valuable  mail  matter.  The  registry  fee  is  ten  cents.  If  regis- 
tered mail  is  lost,  the  sender  is  indemnified  up  to  $  50  for  first- 
class,  and  up  to  $  25  for  third-class  domestic  mail. 

Insurance  of  Parcels.  Mail  sent  by  parcel  post  may  be  insured 
against  loss  upon  the  payment  of  a  fee  of  5  cents  for  value  not 
exceeding  $  25,  or  10  cents  for  value  not  exceeding  $  50,  in  addi- 
tion to  the  postage.     It  may  not  be  registered. 


314 


POSTAGE,   FREIGHT,   AND  EXPRESS  RATES 


1 

5 

1 

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4©= 

Parcels  weighing  4  ounces  or  less  are  mailable  at  the  rate  of  1 
cent  for  each  ounce  or  fraction  of  an  ounce,  regardless  of  distance. 
Parcels  weighing  more  than  4  ounces  are  mailable  at  the  pound 
rates,  a  fraction  of  a  pound  being  considered  a  full  pound. 

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OOOOO      i-H  rH  T-H  i-l  1-1     ,-1  r-H  ^  rH  tH      (M  <N  (N  (M  (N      (M      CO     CO     tJH      -^Ji      iO 

O 

1 
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o 

§§§5g  §g§§s  s;:!^^^  ^2;2:;5::2  i:;  s  g^  ^  s^^  g 

d                          

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2 

n3T3'd'dT3    'OTd'O'ca    'OTJnSTJ'O    'SnO'O'd'C.'CJ.'a.TS.'CJ.'O.TS 

cGcea    scsflta    rtaadq    csacc    fl    c    o    c    rt    c 
f3d::3d:s    3ddsd    s^s^ssp    sajssd    cs    ps    ^    dd.d 

aaaaa  aaaaa  aaaaa  aaaaa*a*a  a  a  a  a 

^(Nco^o  ot^Qooso  -^cc;*S  5S?::$SSS*S'§'^*^*i§*§ 

POSTAGE,  FREIGHT,  AND  EXPRESS  RATES  315 

261.    Rates  for  Foreign  Postage.     The  rates  of  postage  appli- 
cable to  articles  for  foreign  countries  are  as  follows : 

Cents 
Letters  for  Germany,  England,  Ireland,  Newfoundland,  Scotland,  and 

Wales,  per  ounce 2    . 

Letters  for  all  other  countries : 

For  the  first  ounce  or  fraction  of  an  ounce 5 

For  each  additional  ounce  or  fraction  of  an  ounce 3 

Post  cards,  each 2 

Printed  matter  of  all  kinds,  for  each  two  ounces  or  fraction  of  two  ounces  1 
Commercial  papers  (business  documents  without  letters)  : 

For  the  first  ten  ounces  or  less 5 

For  each  additional  two  ounces 1 

Samples  of  merchandise : 

For  the  first  four  ounces 2 

For  each  additional  two  ounces 1 

Parcel  post,  per  pound  or  fraction 12 

Registry  fee  on  all  classes  of  mail,  ten  cents  in  addition  to  the  postage. 

Written  Work 

Compute  the  cost  of  postage  on  the  following : 
Domestic  mail. 

1.  Letter  weighing  IJ  oz. 

2.  Book  weighing  5  oz. 

3.  Book  weighing  19  oz.,  to  a  point  in  the  fourth  zone. 

4.  Newspapers  weighing  26  pounds  mailed  by  publisher. 

5.  Three  separately  wrapped  newspapers  mailed  by  a  person 
not  a  publisher ;  weight,  3  oz.,  5  oz.,  and  8  oz. 

6.  Ten  separately  addressed  printed  circulars,  each  weighing 
li  oz. 

7.  Package  of  merchandise  weighing  3  oz. 

8.  Package  of  seeds  weighing  12  oz. 

9.  Merchandise  weighing  16  lb.  7  oz.,  to  a  point  in  the  sixth 
zone. 

10.  Merchandise   weighing  35  pounds,   to  a -point   130   miles 
distant. 

11.  Registered  letter  weighing  7  oz. 


316  POSTAGE,  FREIGHT,  AND  EXPRESS  RATES 

12.  Books  weighing  11  lb.  9  oz.,  to  a  point  in  the  fifth  zone; 
package  insured.     (Ins.  fee  5^.) 

Foreign  mail. 

13.  Letter  to  Berlin,  weighing  IJ  bz, 

14.  Letter  to  Paris,  weighing  IJ  oz. 

15.  Book  to  Madrid,  weighing  9  oz. 

16.  Package  of  merchandise  samples  weighing  11  oz.,  to 
London. 

Freight  Rates 

A  freight  rate  is  the  charge  made  by  a  railroad  company  for 
conveying  a  specified  quantity  of  property  between  two  stations. 

The  rate  is  usually  stated  in  cents  per  hundred  pounds ;  but  it 
may  be  stated  in  dollars  and  cents  per  ton  or  other  unit  of  weight. 

262.  Factors  Determining  Rates.  Different  rates  are  charged 
on  different  kinds  of  freight,  the  rate  depending  in  general  upon 
two  things : 

a.   The  expense  of  handling. 

Suppose  two  boxes,  each  weighing  100  pounds,  are  sent  by 
freight.  One  is  a  large  box  occupying  40  cubic  feet  of  car  space  ; 
the  other  occupies  only  16  cubic  feet.  The  rate  per  100  pounds 
on  the  first  box  will  probably  be  more  than  on  the  second  because 
fewer  such  boxes  can  be  placed  in  one  car. 

h.   The  risk  of  loss  or  damage. 

Railroads  are  required  by  law  to  pay  for  goods  lost  or  damaged. 
The  rate  will  therefore  depend  upon : 

1.  The  value.  For  example,  the  rate  on  a  prize-winning  cow, 
worth  I  300,  will  be  higher  than  on  a  cow  worth  I  60. 

2.  The  risk  of  damage.  The  rate  on  glassware,  for  example,  is 
higher  than  on  wooden  ware.  Careful  packing  usually  lowers  the 
rate. 

3.  The  risk  of  loss.  The  rate  on  small  packages  which  may 
easily  be  misplaced  or  lost  is  higher  than  on  those  of  larger  size 
having  the  same  value. 

4.  The  risk  of  an  article  damaging  other  articles  in  the  same  car. 


POSTAGE,   FREIGHT,   AND  EXPRESS   RATES 


317 


263.  Classifications.  For  convenience  in  determining  rates, 
commodities  are  grouped  into  ten  different  classifications.  These 
classifications  are  made  by  the  railroads  after  considering  the 
elements  of  cost  of  transportation  and  risk.  When  goods  are  to 
be  shipped  from  one  state  to  another,  the  classification  must  be 
approved  by  the  Interstate  Commerce  Commission. 

A  book  called  a  "  Classification "  is  published,  containing  an 
alphabetical  list  of  commodities  which  can  be  shipped  by  freight, 
together  with  the  classification  in  which  each  commodity  is  placed. 

The  following  list  is  selected  from  a  page  of  a  Classification : 

Notice  that  two  classifications  are  given  for  some  articles.  The 
first  applies  when  goods  are  shipped  in  less  than  car  loads 
(L.  C.  L)  ;  the  second  applies  to  car  load  shipments. 


Cutlery,  blades  or  handles 
plated    or    sterling    silver, 

boxed 1^ 

Cutters,  Sage  Brush  (knife  at- 
tachments for  grading 
machines) : 

In  bundles 2 

In  boxes  or  barrels  .     .     3 

Designs,  Floral,  Artificial 
or  Natural,  dried,  in 
boxes D  1 

Dextrine,  in  bags,  bbls.  or 
boxes,  min.  C.  L.  wt.  30,- 
000  lbs.       .....     2 

Dish- Washing  Machines, 
N.  O.  S., boxed  or  crated.    1 

Formaldehyde,  in  barrels  or 
kegs  or  in  glass  bottles, 
boxed,  min.  C.  L.  wt.  30,- 
000  lbs 2 


C.L. 


5 
Min. 

wt. 
30,000 

lbs. 


Display  Cases,  window  shade, 
boxed  or  crated  ...  1 
Dog  Benches  (for  exhibition 
purposes  only),  K.  D.  flat, 
min.  C.  L.  wt.  30,000  lbs.  4 
Door  Hangers  and  Rail : 
Barn  Door  Hangers  (iron), 

boxed  or  crated    .     .     3 
Barn    Door   Rails   (iron), 

in  bundles  ....     3  . 
Barn  Door    Hanger   Rails 

(wooden),  in  bundles     3 
Parlor       Door       Hangers, 

boxed 2 

Parlor   Door  PI  anger  Rail, 

wooden,  in  bundles    .     3 
Tubing,    for     Barn     Door 

Hanger   Rail,   nested   in 

bundles 4 


C.L. 


B 

5 

Min. 

wt.  30,- 

000  lbs. 


Terms  Explained  :  N.  O.  S.  means  Not  Otherwise  Specified. 

1|  means  One  and  one  half  times  first-class. 

D  1  means  Double  the  first-class  rate. 

C.  L.  means  Car  loads. 

K.  D.  means  Knocked  down,  taken  apart. 


318 


POSTAGE,   FREIGHT,  AND  EXPRESS  RATES 


264.  Freight  Tariff.  The  tariff  is  a  list  of  the  rates  applying 
to  different  classifications  of  freight  when  shipped  between  the 
points  named. 

The  following  illustration  is  selected  from  a  freight  tariff. 


Between 

AND 

Class  Rates  in  Cents  pee  100  Pounds 

i 

1 

i 

1 

i 
•5 

i 

< 
5 

1 

Q 

18 
18 
18 
21 
26 

1 
15 
15 
15 
18 
22 

1 
o 

12 

129 
12 
15 
19 

CO 

o 

11 
11 
11 

135 
17 

Stoddard,  Wis. 
Calvert,  Wis. 
La  Crosse,  Wis. 
Grand  Crossing,  Wis. 
Onalaska,   Wis. 
Lytle,  Wis. 
Trempealeau,  Wis. 
East  Winona,  Wis. 
Winona,  Minn. 

Chicago,  III. 
Group  No.  1 

50 

42 
43 
42 

525 

33 
33 
33 
42 

23 
25 
23 

26 

18 
20 
18 
21 
26 

23 
23 
23 
26 
33 

Springfield,  111. 
Group  No.  2 

53 

St.  Louis,  Mo. 
Group  No.  3 

50 
63 

Danville,  111. 
Group  No.  4 

Cairo,  111. 
Group  No.  4 

80 

65 

52 

33 

Note.     525  means  52 1  cents. 

265.  To  find  the  freight  charge.  The  rates  differ  for  each  of 
the  ten  classifications.  Therefore,  when  a  shipment  of  goods  is 
made,  the  following  steps  are  necessary  to  determine  the  freight 
charge : 

a.  Weigh  the  commodity/. 

b.  Find  its  classification. 

c.  Determine  from  the  tariff  the  rate  applying  to  that  classification 
between  the  points  of  shipment. 

d.  Multiply  the  number  of  hundreds  of  pounds  by  the  rate. 

Example.  A  shipment  of  barn  door  hangers  (crated)  is  sent 
from  Chicago  to  La  Crosse,  Wis.  The  weight  crated  is  185  pounds. 
Find  the  freight  charges. 

Solution.     The  classification  for  less  than  car  load  lots  is  8. 
The  rate  on  third-class  commodities  between  Chicago   and   La  Crosse,  as 
shown  by  the  tariff,  is  33  cents  per  hundred. 

%  .33  freight  rate  per  hundred  pounds 

1.85  number  of  hundreds  of  pounds 
%  .61  freight  charge 


POSTAGE,   FREIGHT,   AND  EXPRESS  RATES  319 

266.  Minimum  Charges.  A  minimum  charge  is  fixed  for  ship- 
ment of  any  commodity  between  two  points.  When  the  charge 
is  computed  and  is  less  than  this  minimum  charge,  the  minimum 
charge  is  made.  The  minimum  charge  is  sometimes  the  third- 
class  rate  per  hundred,  or  it  may  be  an  arbitrarily  fixed  number  of 
cents. 

267.  Car  Loads.  When  goods  are  shipped  in  car  load  lots,  they 
frequently  go  under  a  different  classification  and  at  a  lower  rate. 
Minimum  weights  for  car  loads  are  specified.  For  example, 
36,000  pounds  is  the  minimum  weight  for  a  car  of  door  hangers. 
This  does  not  mean  that  the  car  must  contain  36,000  pounds,  but 
the  shipper  will  be  charged  freight  on  at  least  that  weight,  and 
more  if  the  car  contains  a  greater  weight. 

Example.     Shipped    from    Chicago   to   La  Crosse   a   car   load 
39,000  #  of  door  hangers.     Find  the  freight  charges. 
Solution.     Classification  C.  L.,  5  (see  classification,  page  317). 
Rate,  $  .18. 
390.00  X  1 .18  =  $70.20,  the  freight  charge. 

If  the  door  hangers  weighed  only  32,380  #,  a  charge  would  be 
made  for  the  minimum  weight  of  36,000  #. 

Solution.     Classification,  5. 

Rate,  f^.18  per  100  pounds. 

360  X  $  .18  =  $  64.80,  freight  charge. 

268.  Commodity  Rates.  There  are  some  articles  which  are  not 
listed  in  the  classification,  but  which  have  a  rate  of  their,  own, 
called  a  "commodity  rate."  The  most  important  of  these  com- 
modities are  lumber,  grain,  live  stock,  coal,  coke,  and  hay. 

Written  Work     . 
Find  the  freight  on  each  of  the  following : 

1.  360  #  of  formaldehyde  in  glass  bottles,  boxed,  shipped  from 
St.  Louis,  Mo.,  to  Winona,  Minn. 

2.  500  #  dextrine  in  bags,  shipped  from  Winona,  Minn.,  to 
Danville,  lU. 


320  POSTAGE,  FREIGHT,  AND  EXPRESS  RATES 

3.  260  f  display  cases  (wood  and  wire,  crated),  shipped  from 
Springfield,  111.,  to  Onalaska,  Wis. 

4.  Car  load  of  dextrine  28,000  #,  shipped  from  Winona,  Minn., 
to  Cairo,  111. 

5.  Box  of  silver-plated  cutlery,  60  ^,  shipped  from  Chicago,  to 
La  Crosse,  Wis. 

6.  Box  of  dish  washing  machines,  shipped  from  Chicago  to 
Stoddard,  Wis.     Weight  1T5  #. 

7.  Box  of  parlor  door  hangers,  80  jj^^  shipped  from  Springfield, 
111.,  to  Grand  Crossing,  Wis. 

8.  Flower  design,  35  jf ,  from  Chicago  to  East  Winona,  Wis. 

9.  Car  load  of  iron  door  hangers,  41,350  f^  from  St.  Louis,  Mo., 
to  La  Crosse,  Wis. 

Express  Rates 

269.  The  Classification.  The  express  classification  is  simpler 
than  the  freight  classification,  most  articles  being  unspecified  and 
taking  the  first-class  rate. 

Rate  Scale  Numbers.  The  agent  at  each  express  station  is  sup- 
plied with  a  directory  showing  the  scale  number  to  be  used  in 
computing  the  cost  of  shipment  to  every  express  station  in  the 
United  States.  The  scale  numbers  run  from  1  to  294,  depending 
on  the  distance  between  point  of  shipment  and  point  of  delivery. 

The  following  table  shows  the  rate  scale  numbers  from  the 
Chicago  directory  for  shipment  to  certain  Iowa  points. 

Station  Scale  No.      Station  Soalk  No. 

Burdette 27  Carlisle      ......  26 

Burlington 15  Carnes 39 

Burt •  ^1  Carney 26 

Buxton 21  Carpenter 27 

Q  Carroll 29 

^1  -,7  Casey 30 

Calmar ^'  n  ^      t?  n  oq 

^  1         .  Qo  Cedar  l^alls a6 

Calumet ^^  ^   -,      t»     •  j  i  - 

Cambridge 26  Cedar  Rapids lo 

Campbell 26 


POSTAGE,   FREIGHT,   AND  EXPRESS   RATES 


321 


270.  Schedule  of  Rates.  The  following  table  gives  the  rates  per 
pound  on  shipments  between  points  where  scale  numbers  from  23 
to  33  apply.  The  complete  table  states  the  rates  on  shipments 
weighing  from  1  to  100  pounds. 

Scales  23  to  33 


SCHEDITLB  OF  FlKST-  AND  SeCOND-CLASS  ExPKESS  RaTES  IN  CeNTS 

0 

Scale  Numbers 

EC 

is 

(2 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

1 

i 

S 
M 
Q 

1 

Q 

3 

o 

Q 

5 

1 

O 

to 

3 

1 

i 
5 

i 
3 

i 
o 

o5 

1 

3 

to 

5 

25 

56 

42 

57 

43 

59 

45 

60 

45 

61 

46 

62 

47 

64 

48 

65 

49 

66 

50 

67 

51 

69 

52 

25 

26 

58 

44 

59 

45 

60 

45 

62 

47 

63 

48 

64 

48 

65 

49 

67 

51 

68 

51 

69 

52 

71 

54 

26 

27 

59 

45 

60 

45 

62 

47 

63 

48 

65 

49 

66 

50 

67 

51 

69 

52 

70 

53 

71 

54 

73 

55 

27 

28 

61 

46 

62 

47 

63 

48 

65 

49 

66 

50 

68 

51 

69 

52 

70 

53 

72 

54 

73 

65 

75 

57 

28 

29 

62 

47 

63 

48 

65 

49 

66 

50 

68 

51 

69 

52 

71 

54 

72 

54 

74 

56 

75 

57 

77 

58 

29 

30 

63 

48 

65 

49 

66 

50 

68 

51 

69 

52 

71 

54 

72 

54 

74 

56 

75 

57 

77 

58 

78 

59 

30 

31 

65 

49 

66 

50 

68 

51 

70 

53 

71 

54 

73 

55 

74 

56 

76 

57 

77 

58 

79 

60 

80 

60 

31 

32 

66 

50 

68 

51 

70 

53 

71 

54 

73 

55 

74 

56 

76 

57 

78 

59 

79 

60 

81 

61 

82 

62 

32 

33 

68 

51 

69 

52 

71 

54 

73 

55 

74 

56 

76 

57 

78 

59 

79 

60 

81 

61 

83 

63 

84 

63 

33 

34 

69 

52 

71 

54 

73 

55 

74 

56 

76 

57 

78 

59 

79 

60 

81 

61 

83 

63 

85 

64 

86 

65 

34 

35 

71 

54 

72 

54 

74 

56 

76 

57 

78 

59 

79 

60 

81 

61 

83 

63 

85 

64 

86 

65 

88 

66 

35 

36 

72 

54 

74 

56 

76 

57 

78 

59 

79 

60 

81 

61 

83 

63 

85 

64 

87 

66 

88 

66 

90 

68 

36 

37 

74 

56 

75 

57 

77 

58 

79 

60 

81 

61 

83 

63 

85 

64 

87 

66 

88 

66 

90 

68 

92 

69 

37 

38 

75 

57 

77 

58 

79 

60 

81 

61 

83 

63 

85 

64 

86 

65 

88 

66 

90 

68 

92 

69 

94 

71 

138 

39 

77 

58 

78 

59 

80 

60 

82 

62 

84 

63 

86 

65 

88 

66 

90 

68 

92 

69 

94 

71 

96 

72 

139 

40 

78 

59 

80 

60 

82 

62 

84 

63 

86 

65 

88 

66 

90 

68 

92 

69 

94 

71 

96 

72 

98 

74 

40 

271.    To  find  the  express  charge  for  shipments  of  100  pounds  or 
under. 

a.  Find  the  weight  of  the  commodity. 

b.  Determine  the  classification. 

c.  Find  the  rate  scale  number  applicable  between  the  points  of  ship- 
ment and  deliver!/. 

d.  The  table  of  rates  will  show  the  charge  for  first-  and  second-class 
commodities  weighing  100  pounds  or  less. 

Example.     What  is  the  express  charge  on  a  case  of  medicine 
shipped  from  Chicago  to  Cedar  Falls,  Iowa  ?    Weight,  40  pounds. 

Solution.     Classification,  1. 
Rate  scale  number  (see  table)  23. 


322  POSTAGE,   FREIGHT,   AND  EXPRESS  RATES 

The  schedule  shows  the  charge  under  rate  scale  number  23,  first  class,  40 
pounds,  to  be  78  cents. 

272.    To  find  the  express  charge  for  shipments  over  100  pounds. 

a.  First-class  Rates. 

Find  the  charge  for  a  shipment  of  100  pounds  first  class.  Midtiply  this 
charge  by  the  number  of  pounds  in  the  shipment,  and  divide  by  100. 

Example.  P'ind  the  charge  on  216  pounds  of  first-class  matter 
when  the  rate  scale  number  is  31. 

Solution.  Rate  for  100  pounds,  first-class  matter,  scale  number  31,  is  found 
by  the  complete  table  to  be  $  2 .05. 

100 
Under  the  express  company's  rule  that  all  fractions  of  a  cent  must  be  equal- 
ized as  1  cent,  the  charge  would  be  $4.43. 

h.    Second-class  Rates. 

Multiply  the  first-class  rate  on  100  pounds  by  the  number  of  pounds  in 
the  shipment,  and  divide  by  100. 

Deduct  25%  of  this  result  to  find  the  second-class  charge. 

Example.  What  is  the  charge  on  216  pounds  of  second-class 
matter,  when  the  rate  scale  number  is  31  ? 

Solution.  Charge  for  216  pounds,  first  class,  scale  number  31,  is  $4.43 
(from  previous  illustration). 

75  %  of  $4.43  =  $3.3225,  equalized  as  $3.33. 

Written  Work 

Find  the  charge  for  the  following  shipments  by  express  from 
Chicago : 

1.  26-pound  box  of  cameras  to  Burdette,  Iowa.  Classification 
1  (first  class). 

2.  25  pounds  of  candy  to  Calumet,  Iowa.     Classification  1. 

3.  30  pounds  of  seeds  to  Carpenter,  Iowa.     Classification  2. 

4.  28  pounds  of  telephone  instruments,  unboxed,  to  Casey,  Iowa. 
Classification  1|  times  first  class. 

5.  163  pounds  of  statuary  to  Cedar  Falls,  Iowa.  Classification 
1.     First-class  rate  for  100  pounds,  scale  number  23,  f  1.65. 

6.  191  pounds  of  shrubs  to  Burt,  Iowa.  Classification  2. 
First-class  rate  for  100  pounds,  scale  number  31,  $2.05. 


CHAPTER   XXXII 
DEPRECIATION 

273.  Depreciation  is  the  loss  or  expense  incurred  in  business,  due 
to  the  decline  in  the  value  of  property.  While  repairs  may  be 
made  to  prolong  the  usefulness  of  a  building  or'  a  machine,  there 
is  sure  to  come  a  time  when  the  property  is  either  entirely  useless, 
or  when  it  is  good  business  economy  to  replace  it. 

Suppose  a  machine  which  cost  12400  can  be  used  for  ten  years, 
at  the  end  of  which  time  it  will  be  worth  $  400.  At  the  end  of 
the  ten  years,  when  the  machine  is  replaced,  there  will  have  been 
a  loss  of  $2000  due  to  depreciation.  Unless  a  portion  of  the  de- 
preciation is  charged  as  an  annual  expense,  the  entire  12000  loss 
will  fall  on  the  last  year. 

274.  Methods  of  Computing  Depreciation.  There  are  a  number 
of  methods  of  computing  depreciation.  The  following  are  those 
most  frequently  used  : 

First,  a  fixed  rate,  computed  each  year  on  the  original  value  of 
the  property. 

Second,  a  decreasing  rate,  computed  on  the  original  value  of  the 
property. 

Third,  a.  fixed  rate,  coinputed  on  a  decreasing  value. 

275.  Fixed  Rate  Computed  on  the  Original  Value.  This  is  the 
simplest  method  in  use.  It  can  best  be  explained  by  an  illustra- 
tion. A  printing  press  is  purchased  at  a  cost  of  $8000  and  it  is 
expected  that  this  press  can  be  used  for  ten  years,  when  it  will 
have  a  value  of  $2000.  Therefore,  during  the  ten  years  of  use,  a 
depreciation  of  $6000  will  occur.  This  is  an  annual  depreciation 
of  $  600.     f  600  is  71  %  of  $  8000. 

Therefore  7|-  %  of  the  original  value  is  charged  each  year  as  an 
expense. 

276.  Decreasing  Rate  Computed  on  the  Original  Value  of  the 
Property.     It  is  sometimes  considered  more  reasonable  to  charge 

323 


824  DEPRECIATION 

the  largest  amount  of  depreciation  the  first  year,  gradually  reduc- 
ing it  each  year  thereafter.  It  is  argued  that  a  greater  depreci- 
ation actually  occurs  during  the  first  year  than  during  any  later 
year.  For  example,  an  automobile  is  "second  hand"  after  only  a 
few  months'  use,  and  the  owner  suffers  a  much  greater  loss  from  its 
use  the  first  year  than  he  does  the  second. 

277.  Fixed  Rate  Computed  on  a  Decreasing  Value.  This  method 
results  in  a  similar  decreasing  annual  charge  for  depreciation. 
For  example,  suppose  the  original  value  of  the  property  is  $1200 
and  the  rate  of  depreciation  is  10  %  a  year.  The  depreciation  is 
computed  as  follows: 

$1200.00     Original  value 
.10 


f  120.00     Depreciation  first  year 

i 1200.00 
120.00 


f  1080.00     Decreased  or  carrying  value,  beginning  of  second  year 

AO 

$108.00     Depreciation  second  year 

$1080.00 
108.00 


$972.00     Decreased  value,  beginning  of  third  year 
$97.20     Depreciation  third  year. 

Written  Work 

1.  Find  the  annual  depreciation  on  a  building  worth  $15,560, 
if  4  %  is  charged  off  each  year. 

2.  How  much  is  charged  off  annually  for  depreciation  by  a 
manufacturer  who  owns  property  which  depreciates  at  the  follow- 
ing rates  ? 

Peopeett  Value  Dbpebciatiok  Rate 

Factory  building  $40,000                                               5% 

Machinery  4,800                                             7^  % 

Tools  1,250                                          12i% 

Patents  5,000                                          6^  % 


DEPRECIATION  325 

3.  The  owner  of  a  building  estimates  the  annual  depreciation  as 
3  %  of  its  cost.  The  building  cost  f  4000.  What  is  the  amount 
of  the  annual  depreciation  ? 

The  building  is  rented  at  $40  per  month.  If  the  taxes, 
insurance,  and  other  expenses  amount  to  ^  80  per  year,  what  net 
income  does  the  owner  of  this  property  receive  on  his  investment 
after  allowing  for  depreciation  ? 

4.  It  is  estimated  that  a  machine  costing  %2220  can  be  sold  at 
the  end  of  eight  years  for  $500.  What  per  cent  should  be 
charged  annually  for  depreciation,  and  what  will  be  the  amount  of 
the  annual  depreciation  ? 

5.  Machinery  in  a  factory  cost  $24,000.  Depreciation  is  com- 
puted as  follows : 

10  %  of  the  original  value  the  first  year. 
8  %  of  the  original  value  the  second  year. 
6  %  of  the  original  value  the  third  year. 

3  %  of  the  original  value  the  fourth  year,  and  each  year  there- 
after. 

What  was  the  amount  of  depreciation  charged  off  each  year  for 
five  years  ? 

What  was  the  inventory  value  of  the  machinery  at  the  begin- 
ning of  each  year  ? 

What  was  the  inventory  value  of  the  machinery  at  the  end  of 
12  years? 

6.  A  flour  mill  was  equipped  with  machinery  costing  $  60,000. 
Depreciation  was  computed  at  12J  %  of  its  cost  the  first  year,  8  % 
of  its  cost  the  second  year,  5  %  the  third  year,  2^  %  the  fourth 
year,  and  2  %  each  year  thereafter. 

Find  the  amount  of  depreciation  each  year  for  seven  years. 
What  was  the  inventory  value  of  the  machinery  at  the  beginning 
of  each  year  ? 

Find  the  annual  depreciation  and  the  decreased  value  each  year, 
in  the  following  problems : 

7.  Four  years'  depreciation  on  property  costing  $  3200,  depre- 
ciation computed  at  8  %  of  the  decreased  value. 


326 


DEPRECIATION 


8.  A  manufacturer  was  engaged  in  business  for  10  years.  His 
nincliinery  cost  $  14,500,  and  he  charged  6  %  depreciation  annually 
on  decreased  values. 

9.  Complete  the  following  table,  showing  the  annual  depreciation 
and  decreased  values  per  thousand  dollars  invested  when  depreci- 
ation is  charged  at  various  fixed  rates  on  decreased  values. 
(Correct  to  nearest  mill.) 


1 

2% 

3% 

5% 

1% 

m% 

o 

(«  o 

iz; 
O 

.« 

^ 

(H  Q 

% 

>.  o 

o 

X  o 

§ 

l-i 

5 

t»i 

<1 

1^^ 

% 

i«i 

g«^ 

P5 

^  S  fc, 

a: 

ir. 

1 

ir. 

1 

>  5  h 

h 

> 

P 

^<o 

r* 

1^ 

Q 

> 

1st 

$20 

$980 

2d 

19 

60 

960 

40 

3d 

19 

208 

941 

192 

4th 

18 

824 

922 

368 

5th 

18 

447 

903 

921 

6th 

18 

078 

885 

843 

7th 

17 

717 

868 

126 

Use  the  table  just  prepared  in  solving  the  following  problems. 

10.  Machinery  in  a  factory  cost  $7460.00,  and  depreciation  was 
computed  at  7  %  on  decreased  annual  values.  What  was  the 
depreciation  during  the  fourth  year,  and  the  inventory  value  at 
the  end  of  the  fourth  year  ? 

11.  Cost  of  equipment,  15600.00  ;  depreciation  computed  at 
3  %  on  decreased  annual  values.  What  was  the  depreciation 
during  the  third  year,  and  the  inventory  value  at  the  end  of  the 
third  year  ? 

12.  Cost  of  machinery  $23,746.00;  depreciation  computed  at 
12|  %  on  decreasing  annual  values.  What  was  the  amount  of 
the  depreciation  during  the  sixth  year,  and  the  reduced  value  at 
the  end  of  that  year?  The  depreciation  during  the  sixth  year 
was  what  per  cent  of  the  original  cost  of  the  machinery  ? 


CHAPTER   XXXIII 
ADVERTISING 

During  the  last  fifty  years  the  annual  cost  of  advertising  in  this 
country  has  increased  to  more  than  seven  hundred  million  dollars. 
The  advertising  methods  employed  are  numerous.  The  principal 
mediums  are  newspapers,  magazines,  street  car  signs,  posters, 
electric  signs,  circulars,  booklets,  and  novelties. 

278.  Newspapers.  Newspaper  space  is  sold  by  the  page,  inch, 
and  agate  line.     The  word  "agate"  refers  to  the  size  of  the  type. 

This  is  a  line  of  agate  type. 

An  inch  contains  nine  lines  of  agate  type  when  a  lead  is  placed 
between  each  line;  or  12  lines  when  set  solid.  The  price  varies 
with  the  circulation  of  the  newspaper ;  3  cents  per  inch  per 
thousand  subscribers  is  considered  a  fair  basis  on  which  a  news- 
paper may  determine  its  rates.  On  this  basis,  a  newspaper  with  a 
circulation  of  5000  would  charge  15  cents  per  inch  for  its  space. 
The  larger  newspapers  generally  compute  their  rates  on  the  basis 
of  7  cents  per  line  per  thousand  subscribers,  but  there  are  many 
exceptions  to  this. 


Rate  Card  of  a  Daily  Newspa 

PER 

Display  Eates  per  Agate  Line 

Daily 

Sunday 

Run  of  paper,  5  lines  or  more 

Next  to  reading  matter 

$.40 
.50 
.45 

$.50 
.60 
.55 

Specified  paere 

Discounts  for  Yearly  Contracts 

Lines 

Per  Cent 

Insertions 

2,500  or  more  lines 

5,000  or  more  lines 

10,000  or  more  lines 

10 
25 

28 

26 

52 

312 

327 


328  ADVERTISING 

279.  Magazines.  The  rate  charged  by  magazines  for  advertis- 
ing space  also  depends  upon  the  circulation,  a  fair  basis  being 
considered  J  cent  per  line,  or  •$  1.00  per  page,  per  thousand  sub- 
scribers. Higher  rates  are  charged  for  the  desirable  positions, 
such  as  cover  page,  and  for  printing  in  colors. 


Specimen  Rate  Card  of  the 

-  Magazine 

Katks  per  Issue 

One  page 

$100.00 

Half  page 

50.00 

Quarter  page 

27.00 

Eighth  page 

15.00 

Less  than  }  page,  per  agate  line 

.75 

Inside  cover  page 

150.00 

Back  cover,  3  colors 

350.00 

Three  per  cent  discount  for  cash. 

Forms  close  on  the  10th  day  of  the  month  preceding  date  of  issue. 

One  well-known  magazine  with  a  circulation  of  one  million 
charges  $4000  per  page,  and  there  are  several  magazines  which 
charge  $250  per  page. 

280.  Street  Car  Signs.  Space  is  provided  above  the  windows 
of  most  street  cars  for  printed  signs.  These  signs  differ  in  size, 
but  the  standard  size  is  11  in.  x  21  in.  Some  cards  of  double 
length  are  used  ;  these  are  11  in.  x  42  in.  The  ordinary  rate 
for  street  car  advertising  space  is  50  cents  per  month  per  car  for 
a  half  run,  which  means  six  months  in  all  the  cars,  or  one  year  in 
one  half  the  cars.  It  is  45  cents  a  car  per  month  when  all  cars 
are  used  for  a  full  year.  Exceptions  to  this  rate  apply  in  New 
York,  Chicago,  and  other  large  cities.  The  cards  are  furnished 
at  the  expense  of  the  advertiser. 

281.  Posters.  Posters  are  printed  in  various  sizes,  but  the 
standard  unit  is  a  sheet  28  in.  x  42  in.  The  billboards  are 
usually  about  10  feet  high,  in  order  to  accommodate  4- sheet  posters. 
The  charge  made  for  rent  of  boards  and  posting  signs  depends 
upon  the  size  of  the  city  and  the  desirability  of  the  location.  The 
rates  range  from  4  cents  to  30  cents  a  sheet  per  month.  A  dis- 
count of  5  %  is  usually  given  on  a  contract  for  three  months' 
service,  and  10  %  on  a  contract  for  six  months'  service.     The  cost 


ADVERTISING  329 

of  printing  the  posters  ranges  from  1 J  cents  to  4  cents  per  sheet 
depending  on  the  quality  and  quantity. 

282.  The  Advertising  Agency.  In  many  of  the  larger  cities 
there  are  advertising  agencies  which  assist  advertisers  in  preparing 
copy,  in  directing  advertising  campaigns,  and  in  selecting  the  best 
medium  for  advertising  a  particular  article.  On  the  theory 
that  the  agency  creates  new  business,  publishers  usually  allow 
agencies  a  commission  of  from  10  %  to  15%  of  the  gross  cost  of 
all  advertising  placed  with  them  for  publication. 

283.  Checking  Results.  Large  advertisers  make  special  efforts 
to  determine  the  mediums  which  bring  the  greatest  number  of  in- 
quiries, and  which  result  in  the  most  sales  and  the  largest  amount  of 
profit.  For  this  purpose,  the  advertisements  in  the  various  news- 
papers and  magazines  are  "  keyed  "  ;  for  example,  the  address  may 
be  differentl}^  stated  in  each  medium,  or  different  booklets  may  be 
offered,  so  that  when  the  replies  are  received  in  the  office,  it  will 
be  possible  to  determine  the  medium  which  attracted  the  reader. 
Each  periodical  is  credited  with  the  replies  received  from  its 
readers.  Further  records  are  kept  to  determine  the  value  of  the 
goods  sold  to  the  readers  of  the  periodical,  and  the  profit  result- 
ing therefrom. 

Written  Work 

Refer  to  the  newspaper  rate  card  on  page  327  to  obtair  facts  for  Problems 
1,  2,  and  3. 

1.  On  the  basis  of  nine  agate  lines  to  the  inch,  what  is  the  cost 
of  a  four-inch,  single-column  advertisement?  The  advertisement 
appears  next  to  reading  matter. 

2.  What  is  the  cost  of  a  double-column,  40-line  display  adver- 
tisement, printed  by  request  on  the  financial  page?  How  much 
would  the  same  advertisement  cost  if  printed  on  a  specified  page 
of  the  Sunday  paper?     Can  you  account  for  the  increased  cost? 

3.  A  clothing  store  contracted  for  10,000  lines  to  be  printed  in 
the  course  of  a  year.  8000  lines  were  printed  in  the  daily  editions, 
'"  run  of  paper."  1200  lines  were  printed  in  the  daily  editions  on 
specified  pages,  and  the  balance  appeared  in  the  Sunday  editions 
next  to  the  reading  matter.     What  was  the  total  cost  ? 


330  ADVERTISING 

4.    A  breakfast  food  manufacturer  ran  the  following  amount  of 
advertising  in  the  magazine  whose  rate  card  is  printed  on  page  328. 


January 

1-page 

July     • 

Inside  cover  page 

J'ebruary 

Ipage 

August 

Inside  cover  page 

March 

i  page 

September 

Back  cover 

April 

12  agate  lines 

October 

1  page 

May 

1  page 

November 

1  page 

June 

Inside  cover  page 

December 

ipage 

What  was  the  cost  for  the  year 

•  if  he  paid  cash  ? 

5.    The 

advertiser   in  Problem  4  placed  his  copy  through  an 

agency  which  received  from  the  publishers  121 

%  of  the  gross  cost 

as  its  commission.     How  much  commission  did  the  agency  receive  ? 
How  much  did  the  publishers  receive? 

6.  An  insurance  company  advertised  in  the  street  cars  of  a  city 
in  which  one  of  its  offices  was  located.  There  were  850  cars,  and 
the  insurance  company  contracted  for  a  "  full  run  "  at  the  rate  of 
45  cents  per  month  per  car.  What  was  the  cost  (not  including 
the  cost  of  printing)  ? 

If  the  cards  were  changed  every  two  months,  and  if  400  extras 
were  printed  to  allow  for  "torns"  and  "dirties,"  how  many  were 
required  for  the  year?  What  was  the  cost  of  the  cards  at  ^15 
per  thousand? 

What  was  the  total  cost  of  this  company's  street  car  advertising  ? 

7.  A  manufacturer  advertised  his  product  with  posters.  Each 
poster  was  112'' x  126'^  How  many  sheets  28'' x  42"  to  each 
poster? 

He  signed  a  six  months'  contract  for  250  posters  at  16  cents  per 
sheet  per  month,  posters  to  be  changed  only  when  worn  out,  and 
received  the  customary  10  %  discount.  What  was  the  cost  of  the 
service  ? 

He  purchased  15  %  more  posters  than  were  actually  required  for 
the  boards,  estimating  that  this  number  would  be  necessary  to 
allow  for  damaged  sheets.  What  was  his  printing  bill  at  2J  cents 
per  sheet? 

What  was  the  total  cost  of  the  six  months'  advertising? 

8.  Complete  the  following  table  : 


ADVERTISING 


331 


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332  ADVERTISING 

Which  columns  do  you  think  give  the  best  evidence  as  to 
the  value  of  each  magazine  as  an  advertising  medium  for  this 
product  ? 

Which  is  the  better  evidence  of  the  value  of  an  advertising 
medium,  the  cost  per  reply  or  the  cost  per  sale  ? 

List  these  magazines  in  the  order  of  their  value  as  advertising 
mediums  for  this  particular  advertiser  (on  the  basis  of  per  cent 
of  net  profit). 


CHAPTER   XXXIV 
PROPERTY  INSURANCE 

Property  is  in  danger  of  destruction  from  many  causes ;  insur- 
ance companies  have  been  organized  to  assume  the  risks  of' 
destruction,  thus  relieving  the  owners  from  anxiety  and  loss.  Any 
person  having  a  financial  interest  in  a  property  may  insure  himself 
against  its  loss  or  destruction  by  paying  an  insurance  company 
a  certain  per  cent  of  the  value  of  the  property  insured. 

The  person  who  purchases  insurance  is  called  the  Insured. 

The  company  which  assumes  the  risk  is  called  the  Underwriter. 

The  contract  between  the  insured  and  the  underwriter  is  called 
a  Policy. 

284.  The  Value  of  Insurance. 

a.  In  case  of  loss  the  insured  receives  a  certain  sum,  called  an 
indemnity,  which  wholly  or  partially  repays  his  loss. 

h.  Even  though  the  property  is  not  destroyed,  the  insured  has 
the  security  which  the  insurance  gives. 

c.  Some  wholesale  houses  are  unwilling  to  sell  goods  on  credit 
to  persons  whose  property  is  inadequately  insured. 

285.  Risks  for  which  Insurance  is  Written.  Insurance  companies 
are  organized  to  furnish  protection  against  numerous  kinds  of 
risks.     Some  of  the  most  common  classes  of  insurance  are  : 

Fire. 

Lightning  and  Tornado. 

Marine,  oil  vessels  and  cargoes  at  sea. 

Live  stock. 

Transportation. 

Burglary. 

Plate  Glass. 

Boiler  Explosion. 

Automobile. 

Crop. 

333 


334  PROPERTY  INSURANCE 

The  principles  underlying  all  types  of  property  insurance  are 
the  same,  and  for  the  purposes  of  this  text  fire  insurance  only 
will  be  explained.  It  will  be  understood  that  other  forms  of  in- 
surance may  be  written,  settled,  or  canceled  in  a  similar  manner. 

286.  Process  of  Insuring.  When  a  person  wishes  to  secure  a 
policy  insuring  his  property,  he  should  first  ascertain  the  value  of 
the  property.  To  do  so,  it  may  be  necessary  to  take  an  inventory, 
applying  to  the  goods  a  price  at  which  they  would  sell  in  the 
market  at  the  time  of  taking  the  inventory. 

After  the  valuation  has  been  determined,  the  next  thing  to  de- 
cide is  the  amount  of  insurance  it  is  desirable  to  carry.  If  the 
property  is  insured  at  its  total  valuation,  the  owner  will  bear  no 
loss  in  case  of  fire.  But  since,  in  most  fires,  a  portion  of  the  prop- 
erty is  saved,  it  is  customary  to  insure  only  a  fraction  of  the 
total  valuation.  Thus,  if  a  stock  of  goods  worth  -110,000.00  is  in- 
sured at  1^  of  its  value,  in  case  of  fire  the  insurance  company  will 
pay  all  loss  up  to  17500.00.  If  goods  to  the  value  of  $2500.00  or 
more  are  carried  from  the  building  and  saved,  the  merchant  will 
not  suffer  any  loss.  If  only  11000.00  worth  of  goods  are  saved, 
the  merchant  will  lose  $1500.00. 

It  is  a  matter  of  choice  how  much  risk  the  insured  wishes  to 
take.  If  he  wishes  to  be  free  from  all  risk,  he  should  insure 
his  property  at  its  full  valuation.  Insurance  companies,  how- 
ever, are  rarely  willing  to  insure  property  at  its  full  value. 
Business  men  usually  insure  from  J  to  -|  of  the  valuation  of  their 
property. 

In  some  rural  communities  where  the  fire  protection  is  poor, 
insurance  companies  sometimes  refuse  to  insure  more  than  -I  of 
the  valuation  of  property.  On  the  other  hand,  in  cities  where 
the  fire  protection  is  good  and  the  probability  of  total  loss  is 
comparatively  slight,  people  are  not  inclined  to  insure  a  large 
fraction  of  the  valuation.  To  counteract  this  tendency,  the  in- 
surance companies  frequently  offer  a  lower  rate,  or  price  per 
hundred  dollars  of  insurance  carried,  to  those  who  insure  80  %  or 
more  of  the  valuation  than  they  offer  to  persons  insuring  less 
tlian  80%. 


PROPERTY  INSURANCE  335 

287.  Tne  Cost  of  Insurance.  Insurance  companies  charge  a 
certain  number  of  cents  or  dollars  for  insuring  each  $100.00  worth 
of  property.  Thus,  if  the  insurance  rate  were  60  cents  per  hun- 
dred dollars  of  insurance  carried,  and  you  insured  a  building 
worth  15000.00  at  its  full  value,  the  insurance  cost  would  be  com- 
puted as  follows  : 

f  .60  the  rate  per  $  100  insurance 

50  the  number  of  hundred  dollars  of  insurance  purchased 
$30.00  the  premium,  or  cost  of  the  insurance  per  year 

288.  To  find  the  premium  : 

Multiply  the  valuation  of  the  property  hy  the  fraction  of  the  value 
insured. 

Point  off  two  places  in  this  product^  to  determine  the  number  of 
hundred  dollars  of  insurance  purchased. 

Multiply  hy  the  rate  per  $100. 

Example.  What  is  the  premium  for  insuring,  at  80%  of  its 
value,  a  building  worth  $10,000.00,  if  the  rate  is  90  cents  per  year  ? 

Solution.    $  10,000.00  value  of  the  property 

^  fraction  of  property  to  be  insured 

$8,000.00  insured  value 

$  .90  rate  per  hundred 

80  number  of  hn;mdred  dollars  of  insurance  carried 


$72.00  premium 

289.  Insurance  Rates.  The  insurance  rate  per  hundred  dollars 
per  year  varies  from  $.30  on  brick  dwellings  in  cities,  where  the 
fire  protection  is  good,  to  $  7  or  more  on  very  dangerous  risks, 
such  as  garages  storing  gasoline,  and  buildings  located  in  districts 
where  the  fire  protection  is  poor. 

Thus  it  is  seen  that  the  rate  depends  upon  the  hazard,  or  the 
danger  of  the  property  burning.  This  hazard  is  determined  by 
four  things,  which  are  always  taken  into  account  in  fixing  the  rate 
on  different  pieces  of  property.     They  are: 

a.  The  Construction  of  the  building.  If  it  is  built  of  wood,  a 
higher  rate  is  charged  than  if  it  is  built  of  brick,  or  other  slow- 
burning  material.     If  it  has  many  stories,  so  that  a  fire  starting 


336  PROPERTY  INSURANCE 

near  the  roof  will  be  difficult  to  extinguish,  a  higher  rate  will  be 
charged. 

h.  Its  Occupancy.  If  the  building  is  occupied  by  some  hazardous 
business,  such  as  a  woodworking  mill  in  which  wood  shavings 
accumulate,  or  a  clothes-cleaning  establishment  containing  dan- 
gerous chemicals,  a  higher  rate  will  be  charged  than  if  the  business 
caused  no  particular  hazard. 

c.  Its  Exposure.  By  "  exposure  "  is  meant :  first,  the  distance 
from  other  buildings  from  which  it  might  take  fire  ;  and  second, 
any  hazard  which  might  arise  from  its  being  in  the  neighborhood 
of  a  dangerous  building. 

d.  Its  Protection.  The  rate  will  be  lower  if  the  building  is  close 
to  a  fire  hydrant,  in  a  city  with  an  efficient  fire  department,  or  if 
the  building  is  equipped  with  automatic  sprinklers  which  are 
opened  by  the  heat  from  a  fire.  If  a  night  watchman  is  engaged, 
this  also  may  reduce  the  rate. 

The  rate  depends  also  upon  the  length  of  time  for  which  the  in- 
surance is  purchased. 

290.  Typical  Rates.  The  following  table  will  illustrate  the  rates 
which  apply  on  different  classes  of  property.  On  business  houses 
and  factories  the  rate  is  fixed  after  an  inspection  of  the  property 
made  by  a  representative  of  the  insurance  company.  The 
insurance  companies  of  a  state  frequently  join  in  organizing  an 
"  inspection  bureau  "  which  fixes  the  rates. 

The  rates  on  city  property  will  be  lower  than  those  which  apply 
generally  throughout  the  country,  because  of  the  more  adequate 
fire  protection  of  a  large  city. 

A  City  Insurance  Tariff 

DWELLINGS 

One  Teak, 

PER  $  100 

Brick,  stone,  tile,  cement-block,  or  concrete  dwellings  and  contents  .  %  0.30 
Single  frame  dwellings  and  contents,  detached  not  less  than  50  feet  in 

all  directions 50 

Single  frame  dwellings  and  contents,  detached  not  less  than  25  feet  in 

all  directions 60 

Single  frame  dwellings  and  contents,  detached  50  feet  on  one  side   .     .        .60 


PROPERTY  INSURANCE  337 

One  Year, 
PER  $100 

All  other  frame  dwellings  and  contents,  not  less  than 10.75 

Brick-veneered  or  tile-veneered  dwellings  and  contents 40 

Dwellings  plastered  outside,  with  tile  or  other  noncombustible  roof, 

and  contents 40 

Dwellings  plastered  outside*  with  shingle  or  other  combustible  roof,  rate  same 

as  frame  dwellings. 
Dwellings  in  part  brick  and  frame  rate  as  frame,  subject  to  survey  and  rating 

by  the  board. 
Streets,  without  reference  to  their  width,  to  be  considered  as  cutting  off  charge 

for  exposure. 

BRICK    BUILDINGS    AND    CONTENTS,    OCCUPIED    FOR    APARTMENT    HOUSES    OR 

FLATS 

One  Tear, 
PER  $100 

Three  stories  in  height $0.40 

Four  stories  in  height  and  50  feet  or  less  wide 50 

Five  stories  in  height  and  50  feet  or  less  wide 60 

Six  stories  or  more  in  height  and  50  feet  or  less  wide 75 


BRICK    BUILDINGS    (OTHER    THAN    APARTMENT    HOUSES,    CHURCHES,    SCHOOLS, 
FLATS    AND   WOODWORKING    RISKS)    IN   PROCESS    OF    CONSTRUCTION 

One  Year, 
PER  $  100 

Two  stories  or  less  in  height $0.40 

Three  stories  in  height .50 

Four  stories  in  height 60 

Five  stories  in  height 75 

Over  five  stories  in  height,  add  25  cents  for  each  story. 


SCHOOLHOUSES 

One  Year, 

PER  $  100 

Brick  or  stone,  with  metal,  slate,  or  composition  roof,  and  contents      .    $0.60 

Brick  or  stone,  with  shingle  roof,  and  contents 75 

Frame,  and  contents 1.00 


CHURCHES 

One  Year 

PER  $  100 

Brick  or  stone,  and  contents $0.75 

Frame,  and  contents 1.00 


338  PROPERTY  INSURANCE 

TERM    RATES 

When  policies  are  written  for  several  years,  the  following  will  apply : 

2  years,  1|  annual  rates. 

3  years,  2  annual  rates. 

4  years,  2^  annual  rates. 

5  years,  3  annual  rates.  • 

FARM    PROPERTY 

One  Thbbe  Fivk 

Year,  Yeaes,  Years, 

PKR  $  100  PER  $  100         PER  $  100 

Dwellings,  barns,  outbuildings,  and  contents,  when 

written  under  same  policy $0.50        $1.00        $1.50 

When  farm  barns  and  contents  are  written  with- 
out the  dwellings 75  1.50  2.25 

Written  Work 

Compute  the  premiums  on  the  following  fire  insurance  policies. 
The  proper  rates  will  be  found  by  a  study  of  the  preceding 
tariffs. 

One-year  Policies  —  City  Property 

1.  Single  frame  building,  value  $4000.  No  buildings  nearer 
than  60  feet.     Insured  at  80  %  of  its  valuation. 

2.  Single  frame  dwelling,  value  $5400.  House  on  north,  70 
feet  away;  store  on  south,  25  feet  away.     Insured  at  full  value. 

3.  Brick  dwelling,  value  $6800.  Insured  at  75%  of  its  value. 
Nearest  building,  50  feet. 

4.  Dwelling,  plastered  outside;  shingle  roof.  Value,  $4200. 
Insured  for  $3600.     No  building  nearer  than  35  feet. 

5.  Five-story  apartment  house,  48  feet  wide.  Value,  $36,000. 
Insured  at  |  of  value. 

6.  Four-story  brick  store  in  process  of  construction.  Value, 
$3900:     Insured  at  80  %  of  its  valuation. 

Term  Policies  —  City  Property 

7.  Three-year  policy  on  brick  schoolhouse,  with  tile  roof. 
Value  $40,000.     Insured  at  full  value. 

8.  Five-year  policy  on  frame  church.  Value,  $7500.  Insured 
at  full  value. 


PROPERTY  INSURANCE  339 

Policies  on  Household  Goods  —  City 

9.    Three-year  policy  of  f  1000  on  household  goods  in  frame 
dwelling.     Building  on  north,  10  feet  ;  building  on  south,  60  feet. 

10.  One-year  policy  of  f  500  on  household  goods  in  brick- 
veneered  building. 

Farm  Policies 

11.  One-year  policy  of  ^8500,  covering  dwelling  and  barns. 

12.  Five-year  policy  of  $3000  on  barn  and  silo. 

291.  Insurance  Agent's  Commission.  Local  agents  of  the  fire 
insurance  companies  are  located  in  almost  every  city  and  town. 
They  act  as  the  representatives  of  the  companies,  soliciting  the 
business,  and  collecting  the  premiums.  For  this  service  they 
receive  a  certain  per  cent  of  the  premiums,  usually  varying  from 
15  %  on  mercantile  risks  to  25  %  on  dwellings. 

To  find  the  agent's  commission. 

Example.     Suppose  that  a  store  building  valued  at  $  6000  were  in- 
sured for  J  of  its  value,  the  rate  being  70  cents  per  hundred.     What 
would  be  the  agent's  commission  if  he  received  15%  of  the  premium  ? 
Solution.     |  of^  6000  =  ^  4500,  the  insured  value. 
45  X  $  .70  =  $31.50,  the  premium. 
15%  of  $31,50  =  $4.73,  the  agent's  commission. 

Written  Work 

In  each  of  the  following  problems  find 
The  premium  ; 
The  agent's  commission  ; 

The  amount  of   the  premium   received    by  the    insurance 
company. 

1.  A  one-year  policy  of  $3000  on  a  store  building.  Rate, 
90  cents.     Agent's  commission,  20%. 

2.  A  three-year  policy  on  a  dwelling  valued  at  $6500,  insured 
at  80  %  of  its  valuation.  Rate,  65  cents.  Three-year  policy  for 
2  annual  rates.     Agent's  commission,  18%. 

3.  A  one-year  policy  of  $800  on  household  goods.  Rate, 
50  cents.     Agent's  commission,  15%. 


340  PROPERTY   INSURANCE 

292.  Settlement  of  Losses.  When  a  fire  occurs,  causing  a  small 
loss,  settlement  may  be  made  by  the  local  agent.  When  the  loss 
is  large,  a  special  adjuster  is  sent  by  the  company  to  make  the 
settlement. 

The  adjuster  first  determines  with  the  owner  the  actual  cash 
value  of  the  property  immediately  preceding  the  fire.  This  may 
be  done  by  finding  the  cost  of  the  property  when  new,  and  sub- 
tracting a  certain  amount  for  depreciation ;  that  is,  the  decrease  in 
value  due  to  use,  age,  change  of  style,  or  any  other  cause.  This 
cash  value  is  called  the  sound  value. 

The  adjuster  next  determines  the  value  of  goods  which  were 
saved  from  the  fire.  In  determining  this  value  he  deducts  any 
loss  due  to  damage  by  the  fire,  or  by  water  used  in  extinguishing 
the  fire.     The  property  saved  is  called  salvage. 

It  is  evident  that  : 

Sound  Value  —  Salvage  =  Loss. 

The  companies  pay  this  actual  loss  up  to  the  value  of  the 
insurance  carried. 

Examples. 

1.  Valuation  of   property  by  insured  when   taking 

the  policy 110,000.00 

Insured  for  80  %  of  its  value  ;  Insured  value  .  .  8,000.00 
Sound  value  agreed  upon  by  adjuster  and  insured 

after  allowing  $500  for  depreciation    ....  9,500.00 

Salvage 3,000.00 

Actual  loss        116,500.00 

Since  the  insured  carried  $8000  insurance,  the  loss  would  be 
paid  in  full. 

2.  Valuation  of  property  by  insured  when  taking 

policy $8,000.00 

Insured  for  J  of  its  value;  Insured  value     .     .     .  6,000.00 

Sound  value,  after  deducting  10  %  for  depreciation  7,200.00 

Salvage          500.00 

Actual  loss $6,700.00 


PROPERTY  INSURANCE  341- 

Since  the  insured  carried  only  86000  insurance,  the  company  is 
liable  for  only  $6000  of  the  loss;  the  insured  bearing  the  remain- 
ing 1700  loss. 

In  adjusting  losses,  the  insurance  companies  reserve  the  right 
to: 

a.  Settle  the  loss  as  shown  above  ;  or 

b.  Pay  the  sound  value  of  the  property,  taking  possession  of 
all  the  salvage;  or 

c.  Replace  the  property  by  other  property  of  like  kind  and 
quality. 

Written  Work 

1.  An  apartment  building  worth  -145,000  was  insured  at  80  % 
of  its  valuation.  A  fire  occurred  resulting  in  a  total  loss.  If 
the  sound  value  was  considered  to  be  the  same  as  the  original 
valuation,  how  much  insurance  did  the  owner  of  the  property  re- 
ceive, and  what  was  his  loss  ? 

2.  A  dwelling  valued  at  $  3500.00  was  insured  at  its  full  valua- 
tion. A  fire  resulted  in  a  partial  loss,  the  salvage  being  estimated 
at  11250.00.  If  the  sound  value  of  the  property  was  13325.00, 
how  much  insurance  did  the  owner  of  the  property  receive  ? 

3.  If  the  property  in  Problem  2  had  been  insured  for  $1500.00, 
how  much  insurance  would  have  been  paid  ? 

4.  A  policy  of  $1500.00  was  written  on  a  man's  household 
goods.  When  adjustment  of  the  loss  was  made,  the  following 
facts  were  determined  :  Value  of  household  goods  immediately 
preceding  the  fire,  $1855.00;  salvage,  $575.00.  How  much 
money  did  the  insured  receive  as  a  settlement  ? 

5.  If  the  salvage  in  Problem  4  had  been  $215.00,  how  much 
would  the  insured  have  received  ? 

6.  A  building  worth  $5000.00  was  insured  under  a  five-year 
policy  at  its  full  value.  Four  years  after  taking  the  policy,  the 
house  was  completely  destroyed  by  fire.  In  making  adjustment 
of  the  loss,  it  was  agreed  that  the  sound  value  was  5  %  less  than 
the  insured  value.  How  much  did  the  owner  of  the  house  receive 
in  settlement  ? 


•342  PROPERTY  INSURANCE 

7.  If  the  salvage  in  Problem  6  had  been  $1350.00,  how  much 
insurance  would  the  insured  have  received  ? 

8.  Cost  of  building,  $  6000  ;  insured  for  80  %  of  its  value  under 
five-year  policy  secured  by  the  payment  of  three  annual  rates  of 
75  cents.  Burned  at  end  of  third  year.  Sound  value  determined 
by  deducting  4%  annual  depreciation.  Salvage,  $1200.  Find 
premium  and  loss,  if  any,  to  owner. 

293.  Canceling  Policies.  Both  the  insurance  company  and  the 
insured  have  the  right  to  cancel  an  insurance  policy  at  any  time. 

When  the  policy  is  canceled  by  the  insurance  company^  the 
portion  of  the  premium  to  be  repaid  to  the  insured  is  determined 
pro  rata. 

The  exact  fraction  of  the  time  of  the  policy  which  has  not  ex- 
pired is  determined  and  this  fraction  of  the  premium  is  returned 
to  the  insured. 

Example.  On  Juiy  7,  1917,  the  owner  of  a  building  insured 
his  property  for  one  year.  The  premium  was  $24.00.  On 
September  17,  the  policy  was  canceled  by  the  insurance  company. 
What  rebate  did  the  insured  receive  for  the  unexpired  term  ? 

Solution.  Time  from  September  17,  1917,  to  July  7,  1918,  293  days,  unex- 
pired term  of  policy. 

Ill  of  $24.00  =  %  19.27,  amount  of  ptemium  returned. 

The  table  on  page  267  will  be  of  assistance  in  finding  the  un- 
expired term  of  a  policy. 

Example.  An  insurance  policy  for  one  year  was  purchased 
on  July  9,  and  was  canceled  by  the  company  on  the  17th  of  the 
following  December.  How  many  days  in  the  unexpired  term  of 
this  policy  ?     What  fraction  of  the  premium  will  be  refunded  ? 

Solution.  The  number  of  days  between  December  17  and  July  17  is 
shown  by  the  table  to  be  212.  Subtracting  8,  we  have  204,  the  number  of  days 
from  December  17  to  July  9. 

Iff  of  the  premium  will  be  refunded. 

When  the  policy  is  canceled  by  the  insured^  the  amount  of 
premium  returned  is  determined  by  the  "short  rate."  The  short 
rate  is  an  arbitrary  per  cent  fixed  by  the  insurance  companies, 
and  is  shown  by  a  table,  a  portion  of  which  is  shown  on  page  343. 


PROPERTY  INSURANCE 


34B 


Per  Cents  of  the  Annual  Premiums  to  be  Charged  or  Retained  for 
Periods  less  than  One  Year.  Arranged  by  Days  from  One  to 
Three  Hundred  and  Sixty  Days 


Days 

Per  Cent 

Days 

Peb  Cent 

Days 

Peb  Cent 

Days 

Peb  Cent 

66 

34 

32 

71 

36 

30 

76 

37 

50 

81 

38 

85 

67 

34 

97 

72 

36 

58 

77 

37 

90 

82 

39 

13 

68 

35 

46 

73 

36 

79 

78 

38 

20 

83 

39 

34 

69 

35 

79 

74 

36 

93 

79 

38 

40 

84 

39 

48 

70 

35 

95 

75 

37 

00 

80 

38 

50 

85 

39 

55 

Table  for  Cancellation  of  Term  Risks 


Three- Year  Policies 


For  3  mo.  or  less 20  per  cent  of  term 

Over    3  and  not  exceeding    6  mo 30  per  cent  of  term 

Over    6  and  not  exceeding    9  mo 40  per  cent  of  term 

Over    9  and  not  exceeding  12  mo 50  per  cent  of  term 

Over  12  and  not  exceeding  15  mo 60  per  cent  of  term 

Over  15  and  not  exceeding  18  mo 70  per  cent  of  term 

Over  18  and  not  exceeding  21  mo 75  per  cent  of  term 

Over  21  and  not  exceeding  24  mo 80  per  cent  of  term 

Over  24  and  not  exceeding  27  mo 85  per  cent  of  term 

Over  27  and  not  exceeding  30  mo 90  per  cent  of  term 

Over  30  and  not  exceeding  33  mo 95  per  cent  of  term 

Over  33  mo 100  per  cent  of  term 


premium 
premium 
premium 
premium 
premium 
premium 
premium 
premium 
premium 
premium 
premium 
premium 


Example.  1.  On  October  28,  1917,  a  one-year  policy  for 
12500.00  was  written  on  a  dwelling.  Premium,  112.50.  On 
January  15,  1918,  the  policy  was  canceled  at  the  request  of  the 
insured.     What  rebate  did  the  insured  receive  ? 

Solution.     Time  from  October  28,  1917,  to  January  15,  1918,  79  days. 
The  table  shows  that  38.40%  of  the  premium  is  to  be  retained  when  the 
policy  has  been  in  force  79  days. 
38.40%  of  $12.50  =  14.80. 
$12.50  -  $4.80  =  $7.70,  amount  of  premium  returned. 


344  PROPERTt  INSURANCE 

2.  On  August  12,  1914,  a  three-year  policy  was  written  at  a 
premium  cost  of  #78.00.  On  February  11,  1915,  it  was  canceled 
at  the  request  of  the  policyholder.  What  was  the  amount  of  the 
premium  rebate? 

Solution.  Time  from  August  12,  1914,  to  February  11,  1915,  5  months 
29  days. 

The  table  states  that  when  a  three-year  policy  has  been  in  force  3  months  and 
not  exceeding  6  months,  30  per  cent  of  the  premium  shall  be  retained. 

30  %  of  1 78.00  =  ^  23.40,  amount  of  premium  retained. 

$78.00  -  123.40  =  $54.60,  premium  returned. 

Written  Work 
Find  the  premium  rebates  on  the  following  canceled  policies: 

1.  One-year  policy  of  $2400.00.  Premium,  116.00.  Policy 
written  May  19, 1917  ;  canceled  by  the  company  on  July  29,  1917. 

2.  Same  facts  as  Problem  1,  except  that  the  policy  is  canceled 
at  the  request  of  the  policyholder. 

3.  Three-year  policy,  dated  July  23,  1917.  Face  of  policy, 
$  3600.00.  Rate,  65  cents,  three-year  policy  being  written  for  term 
rates.  Policy  canceled  at  the  request  of  the  policyholder  on 
October  7,  1918. 


CHAPTER   XXXV 
TAXATION 

294.  Purpose  of  Taxation.  The  national  government  requires 
money  to  support  the  army  and  navy,  to  pay  the  salaries  of  gov- 
ernment employees,  to  pay  pensions,  and  to  finance  other  activities 
carried  on  by  the  nation.  During  a  recent  year,  Congress  appro- 
priated $  1,098,678,788  for  the  annual  budget. 

The  state  governments  require  money  for  the  expense  of  their 
officers,  and  to  support  their  various  institutions,  schools,  universi- 
ties, asylums,  and  penitentiaries. 

The  counties  require  money  for  the  building  of  bridges,  the 
trial  of  criminal  cases,  the  salaries  of  officers,  the  relief  of  the 
poor,  etc. 

Cities  must  pay  for  police  and  fire  protection,  care,  of  streets, 
etc. 

School  districts  contribute  to  the  support  of  the  public  schools. 

The  money  required  for  all  these  expenses  is  raised  by  taxes, 
licenses,  fees,  assessments,  and  fines. 

295.  A  tax  is  a  sum  of  money  levied  by  the  proper  officers  of  a 
government  to  defray  government  expenses. 

The  funds  of  the  national  government  are  raised  largely  in 
three  ways: 

Customs  Duties  on  Imports  ; 
Internal  Revenue  ;  ' 

Income  Tax. 
The  funds  of  the  state  and  local  governments  are  raised  largely, 
by  direct  taxes  on  real  estate  and  personal  property. 

State  and  Local  Taxes 

296.  Taxable  Property.  The  amount  of  property  tax  paid  by 
any  individual  to  state  and  local  governments  depends  upon  the 
value  of  the  property  which  he  owns  and  the  tax  rate. 

345 


346  TAXATION 

Real  estate  consists  of  land  and  buildings. 

Personal  property  consists  of  movable  property,  such  as  mer- 
chandise, furniture,  machinery,  live  stock,  cash,  notes,  stocks, 
bonds,  and  mortgages. 

297.  Determining  the  Assessed  Value  of  Property.  The  value  of 
each  person's  taxable  property  is  determined  by  the  assessor.  The 
assessed  value  is  usually  a  fractional  part  of  the  real  value. 

For  example,  in  a  certain  state,  property  is  assessed  at  ^  of  its 
real  value.  Jones  owns  a  farm  which  the  assessor  considers  to 
have  a  real  value  of  $30,000.     He  therefore  assesses  it  at  ilO,000. 

Although  the  law  gives  the  assessor  the  power  to  determine  the 
taxable  value  of  property,  property  owners  usually  have  the 
privilege  of  appearing  before  a  Board  of  Equalization  to  prove  a 
claim  that  their  property  has  been  assessed  at  too  high  a  valuation. 
The  Board  of  Equalization  judges  between  the  values  fixed  on 
property  by  the  assessor  and  by  the  owner. 

298.  The  Tax  Rate.  The  tax  rate  may  be  expressed  in  several 
ways,  the  most  common  of  which  are : 

*A  per  cent ; 

A  certain  number  of  mills  on  each  dollar  of  assessed  valuation  ; 
A  certain  number  of  dollars  or  cents  on  each  hundred  dollars 
of  assessed  valuation. 

The  following  tax  rates  are  equivalent: 

1.6%; 

16  mills  (on  the  dollar)  ; 

11.60  (on  each  hundred  dollars). 

299.  To  find  the  amount  of  tax.  To  find  the  amount  of  tax  to 
be  paid  by  any  property  owner : 

Multiply  the  assessed  value  of  the  property  hy  the  tax  rate. 
(a)    When  the  rate  is  stated  as  a  per  cent. 

Example,  Bennet's  property  is  assessed  at  1 3000 ;  the  tax  rate 
is  1.6  %. 

Solution.  $  3000  assessed  valuation 

.016  tax  rate 
$48.00  tax 


TAXATION  347 

(J)  When  the  rate  is  stated  as  a  certain  number  of  mills  on 
the  dollar. 

Example.  Taylor's  property  is  assessed  at  t3800.  The  rate 
is  24  mills. 

Solution.  $  3800  assessed  valuation 

.024  tax  rate  in  mills 
$91.20  tax 

(c)  When  the  rate  is  stated  as  a  certain  number  of  dollars  on 
each  hundred  dollars  of  assessed  value. 

Example.  Finch's  property  is  assessed  at  f  5470.  The  tax 
rate  is  '11.95. 

Solution.        $  1.95  the  rate  per  hundred  dollars 

54.70  the  number  of  hundreds  of  dollars  assessed  value 
$106.67  the  tax 


Oral  Work 

1.  State  each  of  the  following  tax  rates  in  two  other  ways : 

3.6%  27  mills  ^12.83 

2.  A  certain  state  assesses  property  at  f  of  its  real  value. 
What  is  the  assessed  value  of  a  house  worth  f  5000  ?  Of  a  factory 
worth  $15,000  ?     Of  a  building  worth  |4000  ? 

3.  Dickinson  has  a  house  assessed  at  f2000.  The  rate  is 
2.5%.     What  is  his  tax? 

4.  Barnes  has  a  store  building  assessed  at  $  3000  and  a  house 
assessed  at  •!  2000.     The  tax  rate  is  30  mills.     What  is  his  tax  ? 

5.  If  property  is  assessed  at  ^  of  its  real  value,  what  is  the 
assessed  value  of  a  city  lot  worth  $  1200  ?  How  much  tax  will 
the  owner  pay  if  the  tax  rate  is  22  mills  ? 

6.  Property  valued  at  f  6000  is  assessed  at  ^  oi  its  value  and 
taxed  at  a  rate  of  $  2.50.     What  tax  does  the  owner  pay  ? 

7.  Three  men  living  in  different  cities  were  comparing  their 
tax  rates.  A's  rate  was  $  3.56  ;  B's  rate  was  28  mills  ;  C's  rate 
was  3.14%.  Which  had  the  largest  rate?  How  much  tax  should 
each  pay  on  an  assessed  value  of  f  2000  ? 


348 


TAXATION 


8.  Bailey  owns  property  worth  $  15,000  and  is  taxed  $  4.50  per 
hundred  dollars  on  ^  of  the  real  value.  Osborne  owns  property 
worth  $  15,000  and  is  taxed  32  mills  on  -J  the  real  value.  Which 
pays  the  larger  tax  ?     How  much  does  each  pay  ? 

9.  Powell  pays  3  %  on  ^  of  the  real  value  of  his  property. 
What  per  cent  of  the  value  of  his  property  does  he  pay  annually 
as  taxes  ? 

10.  A  loaned  money  at  6  %  and  took  a  mortgage.  Since  a 
mortgage  is  personal  property,  it  is  taxable.  The  mortgage  was 
taxed  at  a  rate  of  f  4  on  ^  the  real  value.     What  per  cent  of  the 


value  of  the  mortgage  did  A  pay  annually  as  taxes  ? 
his  per  cent  of  net  income  on  the  loan  ? 


What  was 


Written  Work 
1.    Complete  the  following  table  : 


liEAL  Value  of 
Property 

Fraction  of 
Value  Assessed 

Assessed  Value 

Rate 

Tax 

$16,250 

i 

$5.42 

7,920 

i 

3.18% 

22,000 

i 

$2.89 

960 

i 

64  mills 

4,000 

i 

2.92% 

2.  Hill  rents  his  house  for  130.00  per  month.  The  house  cost 
him  13850.00.  What  is  the  per  cent  of  net  profit  on  his  invest- 
ment, after  paying  the  following  annual  expense  ? 

Insurance,  $15.40. 

Repairs,  $60.00. 

Taxes :  Property  assessed  at  ^  its  value  and  taxed  at  16.23  per 
hundred  dollars. 

300.  To  determine  the  tax  rate.  Each  of  the  taxing  govern- 
ments (state,  county,  township,  city,  school  district,  etc.)  pre- 
pares a  budget  or  estimate  of  the  money  needed  for  the  following 
vear. 


TAXATION  349 

The  assessed  value  of  the  property  available  for  taxes  is  found 
from  the  assessors'  lists. 

The  amount  of  funds  needed,  divided  by  the  assessed  value  of 
the  property,  gives  the  rate  which  must  be  levied  in  order  to  obtain 
the  required  amount. 

The  rates  for  the  state,  county,  city,  school  district,  etc.,  are 
added  to  form  a  single  rate. 

The  following  illustration  shows  the  method  of  determining  a 

tax  rate. 

State   Tax 

State  budget $  3,600,000 

Assessed  value  of  the  property  in  the 

state $1,000,000,000 

$  36,000  ^  1 1,000,000,000  =    .36  %  state  rate 

County  Tax 

County  budget $30,000 

Assessed  value  of  the  property  in  the 

county $4,000,000 

$  30,000  ^  14,000,000  =    .75  %  county  rate 

City  Tax 

City  budget     .     • $12,000 

Assessed  value  of  property  in  the  city    .  $  1,000,000 

$12,000  -4-  $  1,000,000  =  1.20%  city  rate 

School  Tax 

School  district  budget $24,000 

Assessed  value  of  the  property  in  school 

district $1,000,000 

$24,000  H-  $  1,000,000  =  '2A0  %  school  tax  rate 
4.71  %  total  tax  rate 

Example.  Mr.  Owen  has  a  building  worth  115,000.00,  which 
is  assessed  at  J  of  its  real  value.  What  is  the  tax  on  the  build- 
ing at  the  above  rate  ? 

Solution.     Assessed  value,  $  5,000.00. 
Rate,  4.71  %. 
.0471  X  $5,000.00  =  $235.50,  tax. 

Oral  Work 
Explain  why  the  tax  rate  in  your  city  may  be  different  from 
the  rate  in  a  neighboring  city. 


350  TAXATION 

Written  Work 

1.  Find  the  tax  rate  (approximate). 
State  budget,  12,850,000. 

Assessed  value  of  property  in  the  state,  11,450,000,000. 

State  rate? 

County  budget,  $  33,000. 

Assessed  value  of  property  in  county,  $5,600,000. 

County  rate  ? 

City  budget,  f  14,800. 

Assessed  value  of  property  in  city,  11,345,000. 

City  rate  ? 

School  district  budget,  $  32,500. 

Assessed  value  of  property  in  school  district,  f  1,345,000. 

School  tax  rate  ? 

Total  rate  ? 

2.  The  following  is  the  tax  rate  in  the  town  of  M. 

State  tax  $   .QO 

County  tax  1.25 

Township  tax  .26 

City  tax  2.18 

School  district  tax  2.86 

$7.15 
In  this  town,  property  is  assessed  at  ^  of  its  real  value. 
Snyder  owns  the  following  property : 

Rkal  Values 

Residence  16,500.00 

Store  4,950.00 

Office  building  13,000.00 
What  is  his  total  tax  ? 

3.  How  much  of  this  tax  goes  to  the  state,  and  how  much  to 
each  of  the  other  taxing  units  ? 

4.  What  per  cent  of  his  tax  goes  to  each  of  the  taxing  units  ? 

5.  The  assessed  value  of   Miller's   real   estate  is   $13,395.00. 
What  is  his  total  tax  ? 

6.  How  much  school  tax  does  Miller  pay  '^ 


CHAPTER   XXXVI 
THE   INCOME  TAX 

301.  Basis  of  the  Tax.  The  income  tax  bill,  which  became  a 
law  on  October  3,  1913,  and  which  was  amended  Sept.  8,  1916, 
places  a  tax  on  all  net  incomes  in  excess  of  $3000.00  a  year  in  the 
case  of  single  persons,  whether  adults  or  minors,  and  in  excess  of 
$4000.00  per  year  in  the  case  of  the  head  of  a  family.  The 
normal  tax  is  based  on  the  excess  only.  The  tax  is  levied  on 
American  citizens  living  in  this  country  and  abroad,  on  aliens  liv- 
ing in  the  United  States,  on  corporations,  joint-stock  companies 
or  associations,  and  insurance  companies.  Exemptions  are  not 
allowed  except  in  the  case  of  individual  citizens. 

302.  Gross  Income.  Gross  income  consists  of  salaries,  wages, 
interest,  rent,  and  all  profits  or  income  arising  or  accruing  from 
whatsoever  source,  with  the  exception  of  interest  on  the  bonds  of 
the  United  States  government  and  its  political  subdivisions. 
Property  acquired  by  gift  or  bequest,  and  the  proceeds  of  life 
insurance  policies  paid  on  the  death  of  the  insured,  are  not  con- 
sidered as  income. 

303.  Net  Income.  Only  the  net  income  is  taxed.  The  net 
income  for  the  purpose  of  the  tax  is  found  by  deducting  from 
the  gross  income  all  necessary  expense  actually  paid  in  carry- 
ing on  the  business  (but  not  personal,  living,  or  household 
expenses) ;  interest  paid  on  indebtedness ;  taxes ;  fire  losses 
not  covered  by  insurance  or  otherwise,  loss  from  bad  debts,  if 
actually  charged  off;  a  reasonable  depreciation  on  the  value  of 
property. 

304.  The  Normal  Tax.  The  rate  of  the  normal  tax  is  2  %  of 
the  net  income  above  the  amount  exempted. 

351 


352  THE   INCOME  TAX 

Example.  A  married  man  living  with  his  wife  has  a  net  income 
of  S7000.     How  much  income  tax  is  he  required  to  pay? 

Solution.  $7000  Net  income 

4000  Exemption 
$3000  Taxable  income 

.02  Normal  rate 
$     60  Income  tax 

305.  The  Additional  or  Super  Tax.  In  addition  to  the  normal 
rate  of  2  %  levied  on  incomes  in  excess  of  the  exemption,  an  addi- 
tional tax  is  assessed  on  large  incomes. 

The  following  table  gives  the  additional  rates  charged  on  the 
portions  of  net  income  which  exceed  specified  amounts. 

On  the  amount  by  which  the  total  net  income  (not  deducting  the  $3000  or 
$4000  exemption  applying  to  the  normal  tax). 

exceeds  $  20,000  but  does  not  exceed  $ 
exceeds  40,000  but  does  not  exceed 
exceeds  60,000  but  does  not  exceed 
exceeds  80,000  but  does  not  exceed 
exceeds  100,000  but  does  not  exceed 
exceeds  150,000  but  does  not  exceed 
exceeds  200,000  but  does  not  exceed 
exceeds  250,000  but  does  not  exceed 
exceeds  300,000  but  does  not  exceed 
exceeds  500,000  but  does  not  exceed 
exceeds  1,000,000  but  does  not  exceed 
exceeds  1,500,000  but  does  not  exceed 
exceeds     2,000,000 

Example.  Dudley,  an  unmarried  man,  has  a  net  income  of 
1125,000  per  year.     What  is  his  income  tax? 

Solution.  $125,000  Total  net  income 

3,000  Exemption 
$122,000  Basis  of  normal  tax 

29^0  of  $122,000 $2440  Normal  tax 

1%  of  $  20,000  (excess  between  $20,000  and  $40,000)  200  Additional  tax 

l^fo  of  $  20,000  (excess  between  $40,000  and  $60,000)  400  Additional  tax 

3%  of  $  20,000  (excess  between  $60,000  and  $80,000)  600  Additional  tax 

4^0  of  $  20,000  (excess  between  $80,000  and  $100,000)         800  Additional  tax 
59ij  of  $  25,000  (excess of  total  net  income  over  $100,000)     1250  Additional  tax 

$5690  Total  tax 

306.  Collection  at  the  Source.  The  law  provides  that  the  tax 
on  incomes  derived  from  interest,  rent,  salaries,  wages,  and  other 


S     40,000 

1% 

60,000 

2^0 

80,000 

3% 

100,000 

4^0 

150,000 

5% 

200,000 

6-^0 

250,000 

7fo 

300,000 

8% 

500,000 

9% 

1,000,000 

109^0 

1,500,000 

\\oJo 

2,000,000 

12<fo 

IS^o 

has  a  net  income 

THE  INCOME  TAX  •  353 

fixed  annual  gains  payable  to  an  individual,  shall  be  deducted  by 
the  debtor  and  paid  by  him  to  the  government.  This  is  called 
collection  at  the  source. 

No  deduction  is  made  unless  the  total  interest,  rent,  or  salary, 
etc.,  paid  to  one  individual  during  the  year  exceeds  $3000.00.  If 
the  annual  payment  exceeds  $3000.00,  2%  of  the  total  is  deducted, 
unless  the  creditor  files  with  the  debtor  a  certificate  claiming  the 
exemption  of  $3000.00  or  $4000.00  provided  by  law.  When  ex- 
emption is  claimed,  2  %  is  deducted  from  the  amount  in  excess  of 
the  exemption. 

Examples.  1.  Jones  loans  $5000  to  Smith  at  6%  interest. 
The  annual  interest  is  $300.  Since  the  annual  payment  is  less 
than  $3000,  Smith  pays  Jones  the  full  amount  of  the  interest 
without  deduction. 

2.  Jones  loans  Smith  $60,000  at  6%  interest.  The  annual 
interest  is  $3600. 

a.  Jones  has  already  claimed  his  exemption  on  some  other  in- 
come, and  is  therefore  not  permitted  to  file  a  certificate  of  exemp- 
tion with  Smith.  Smith  therefore  deducts  2%  of  $3600,  or  $72, 
and  pays  Jones  the  balance,  $3528.  Forms  are  provided  for 
notifying  the  collector  of  internal  revenue,  who  later  sends  Smith 
a  bill  showing  the  amount  to  be  paid. 

h.  Jones,  being  a  single  man,  and  not  having  filed  certificate  of 
exemption  elsewhere,  files  a  certificate  with  Smith,  claiming  an 
exemption  of  $3000.  Smith  deducts  2%  of  $600  (the  excess  of 
the  interest  over  $  3000)  and  pays  Jones  the  balance,  $  3588.  He 
notifies  the  collector  of  internal  revenue  that  he  has  deducted  the 
$12  tax  at  the  source,  and  on  receiving  a  bill  from  the  collector 
he  forwards  all  money  so  retained. 

c.  If  Jones  were  a  married  man,  he  could  file  a  certificate  of 
exemption  for  $4000.  Smith  would  send  this  certificate  to  the 
government  collector,  and  pay  Jones  the  entire  amount  of  the 
interest,  $3600. 

In  illustration  (?,  Jones  has  not  exhausted  his  exemption.  He 
can  claim  a  $400  exemption  from  some  other  debtor. 

The  certificates  are  forwarded  by  the  debtors  to  the  collector 


354  THE   INCOME  TAX 

of  internal  revenue  so  that  the  government  can  check  up  the 
exemptions  and  prevent  any  person  from  claiming  more  than  his 
legal  right.  If  a  person  files  certificates  at  the  source,  claiming 
greater  exemption  than  he  is  entitled  to,  he  becomes  liable  to  a 
fine  of  $  300. 

Collecting  at  the  Source  from  Corporations.  If  the  debtor  is  a 
corporation,  2  %  of  all  interest  must  be  deducted,  whether  the 
annual  amount  exceeds  ^3000  or  not,  unless  a  certificate  of  ex- 
emption is  filed. 

Example.  Osborne  owns  a  bond  of  f  1000,  payable  by  the 
Franklin  Company,  a  corporation,  and  bearing  6  %  interest,  pay- 
able semi-annually.  July  1,  he  clips  the  interest  coupon  for  $  30, 
and  presents  it  to  his  bank  for  collection.  The  coupon  must  be 
accompanied  by  a  certificate  which  states  either  that  Osborne  claims 
exemption,  or  that  he  does  not  claim  exemption. 

a.  Osborne  is  married:  he  attaches  a  certificate  to  the  coupon 
claiming  exemption  of  $  4000.     He  will  receive  the  full  $  30. 

h.  Although  Osborne  is  entitled  to  an  exemption  of  f  4000,  he 
presented  other  coupons  yesterday  for  $  4000  and  claimed  his  full 
exemption  on  them.  He,  therefore,  attaches  a  certificate  to  this 
coupon,  stating  that  he  does  not  claim  further  exemption,  and  2  % 
of  the  $  30  is  deducted. 

307.  The  Corporation  Tax.  Corporations  are  required  to  pay 
a  tax  on  their  entire  net  income  without  any  exemption.  They 
are  subject  to  the  normal  tax  of  2  %  only. 

Example.  The  Hayes  Corporation  had  a  net  income  during 
the  year  1916  of  ^  15,250.      What  was  its  tax  ? 

Solution.     2  %  of  |  15,250  =  $  305.00,  the  corporation  tax. 

Since  the  corporation  has  paid  the  tax  on  its  net  earnings,  the 
individual  stockholder  is  permitted  to  deduct  the  dividends  re- 
ceived from  stock  from  his  gross  income,  wlien  determining  his 
net  income,  on  which  the  normal  tax  is  computed.  But  dividends 
must  be  added  to  the  income  to  determine  the  basis  of  the  addi- 
tional .tax.  This  provision  is  made  so  that  taxes  will  not  be  paid 
twice  on  the  same  income. 


THE  INCOME  TAX  355 

Written  Work 
Find  the  income  tax  on  the  following : 

1.  Net  income,  $  5000  ;  single  man. 

2.  Net  income,  f  5000  ;  married  man. 

3.  Net  income,  $  63,000  ;  single  man. 

4.  Net  income,  8  63,000;  married  man. 

5.  Net  income,  $  126,000  ;  married  man. 

6.  Net  income,  $  580,000 ;  single  man. 

7.  Find  the  net  income  and  the  income  tax  (married  mar.)' 
Salary,  $3500;  rent  on  buildings  owned  by  him,  81250;  inter- 
est on  money  loaned  by  him,  I  600. 

He  pays  81400  interest  on  money  which  he  has  borrowed; 
repairs,  insurance,  and  depreciation  on  rented  property,  f  165; 
state  and  local  taxes,  f  255. 

8.  Find  the  net  income  and  the  tax  (single  man). 

Salary,  $  5000 ;  proiit  from  sale  of  land,  $  2400  ;  royalties  on  a 
patent,  $  2875. 

During  the  year,  a  fire  caused  a  loss  of  $  14,000  partially  covered 
by  a  8 10,000  insurance  policy.     State  and  local  taxes,  $  420. 

9.  Find  the  net  income  and  the  tax  (married  man). 

Cost  of  goods  sold  during  the  year      .    8 146,000 
Gross  sales 197,000 

Rent,  insurance,  wages  of  employees,  and  other  business  ex- 
penses, $  14,000.  Loss  from  bad  debts,  actually  incurred,  deter- 
mined, and  charged  off,  $  985.  He  had  borrowed  $  5000,  on  which 
he  paid  a  year's  interest  at  5  % .  His  store  building  was  worth 
1 8000  and  he  estimated  the  annual  depreciation  at  2  %  of  the 
value  of  the  building. 

10.  Carter,  a  married  man,  owned  a  factory  which  made  a  net 
annual  profit  of  1 15,000.  Rent  on  houses  owned  by  him,  8  3400  ; 
repairs,  taxes,  and  depreciation  on  rented  property,  $  815.  He 
received  $  1800  dividends  from  a  corporation  which  had  already 
paid  the  corporation  tax.  He  had  loaned  $  25,000  to  Mitchell  for 
a  year  at  6  % . 

What  was  his  gross  income,  net  income,  and  total  income  tax  ? 


356  THE   INCOME  TAX 

11.  Potter,  a  single  man,  had  $  80,000  invested  in  bonds  pay- 
ing 5  %  interest.  What  was  the  annual  interest  on  these  bonds  ? 
How  much  would  his  annual  income  tax  amount  to  ?  If  he  filed 
certificates  for  his  full  legal  exemption,  how  much  of  the  tax  would 
be  paid  at  the  source  ? 

12.  Walker,  a  married  man,  had  the  following  gross  income, 
expenses,  and  losses  during  the  year : 

G-ross  Income 

Salary,  $  4000 ;  interest  on  money  loaned  on  notes,  f  750 ; 
dividends  from  stocks  of  a  corporation,  $  1200  ;  gain  on  sale  of 
farm,  $  3200 ;  interest  on  bonds,  I  5200. 

Expenses  and  Losses 
Interest  on  money  borrowed,  i  60  ;  taxes,  $  945. 
What  was  his  gross  income  ? 
What  was  his  net  income  ? 
What  was  his  total  income  tax  ? 

If  he  filed  certificates  when  collecting  the  bond  coupons,  claim- 
ing his  full  exemption,  how  much  of  his  tax  was  paid  at  the  source? 

13.  How  much  income  tax  is  paid  by  corporations  making  net 
profits  of  $  1800  ?  $  2500  ?  1 74,000  ?  $  825,000  ? 


CHAPTER    XXXVII 
CUSTOMS   DUTIES 

308.  Tax  on  Imports.  The  national  government  collects  a  tax 
from  persons  who  import  certain  kinds  of  merchandise  into  the 
United  States  from  foreign  countries.  The  taxes  thus  imposed 
and  collected  are  called  Customs  Duties. 

The  process  of  importing  goods  is,  very  briefly,  as  follows : 

The  foreign  shipper  prepares  an  invoice  of  the  goods,  showing 
their  value  in  the  coinage  of  the  exporting  country. 

Invoices  of  goods  with  a  value  of  more  than  jfelOO.OO  are  certi- 
fied by  the  United  States  consul  in  the  foreign  city.  The  consul 
retains  one  copy  of  the  invoice  and  sends  another  copy  to  the 
collector  of  the  United  States  port  to  which  the  goods  are  shipped. 

When  the  goods  are  delivered  to  the  steamship  company,  the 
shipper  receives  a  bill  of  lading,  which  is  a  receipt  for  the  mer- 
chandise. This  bill  of  lading  and  an  invoice  are  sent  to  the 
American  importer. 

When  the  goods  arrive  at  port  in  this  country,  the  importer 
presents  the  invoice  and  the  bill  of  lading  at  the  custom  house, 
pays  the  duty,  and  receives  his  merchandise. 

Customs  duties  are  of  two  kinds  :  ad  valorem  and  specific. 

309.  Ad  Valorem  Duties.  "  Ad  valorem  "  means  :  according  to 
value.  When  an  ad  valorem  duty  is  placed  on  goods,  the  tax  is  a 
certain  per  cent  of  the  value  of  the  merchandise.  Ad  valorem 
duties  are  not  computed  on  fractions  of  a  dollar.  If  the  cents 
are  less  than  fifty,  they  are  dropped ;  if  fifty  or  more,  they  are  con- 
sidered an  additional  dollar. 

To  compute  ad  valorem  duty : 

Reduce  the  value  of  the  goods  stated  in  foreign  money  to  United 
States  money.     Multiply  the  value  hy  the  tariff^  rate. 

357 


358 


CUSTOMS  DUTIES 


CONSUMPTION  ENTRY.  't^:^M^K. 

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MERCHANDISE  IMPORTED  BY QsT:£:fA^...^^r?'S:?^^  _ 

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on  ..QA{i/...'kT. ,  Invoice  No.  .?::/<?..?....,  Dated  at  VefJk^u^i.^*^  ...'S^^^^. ,  on  ./7laL^..t:./,J^/j/l 

Forwarded  from  ...^....^. ■;:--.-•.:.•  V"'!*''.  I- T-  No-^^.^.^. ,  Dated  ..^^^^..9^^./^/.>^.. 


e  out  this  line  for  direct  i 


PACKAGES  AND  CONTENTS. 


;K 


^9^/fc 


M 


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d.^J 7.U-:0..4^. 


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Estimated  duty  paid,  %..^.0.i. 
Bond,  Cat.  No _. 


33 


CUSTOMS  DUTIES  359 

The  Secretary  of  the  Treasury  proclaims  the  value  of  foreign 
coinage  in  terms  of  United  States  money,  and  the  most  recent 
proclamation  is  used  as  the  basis  of  money  reduction.  A  copy  of 
such  a  proclamation  will  be  found  on  page  234. 

Example.     What  is  the  duty  on  an  importation  of  woolen  dress 
goods  valued  at  <£  30,  the  tariff  rate  being  35  %  ad  valorem  ? 
Solution.     Value  of  shipment  in  foreign  coinage,  £  30. 
Value  in  United  States  coinage,  $  146.00. 
35  %  of  $  146.00  =  $  51.10,  amount  of  duty. 

310.  Specific  Duties.  Specific  duties  are  levied  according  to  the 
quantity  of  the  goods  imported,  without  respect  to  their  value. 
The  rate  is  usually  stated  as  a  certain  number  of  cents  per  pound, 
per  hundred  pounds,  per  ton  (2240  lb.),  per  yard,  or  other  standard 
of  measure.     Allowance  is  sometimes  made  for  tare  and  breakage. 

To  compute  specific  duty.  When  the  metric  system  of  measure- 
ment is  used  in  the  foreign  invoice,  the  quantity  must  be  reduced 
to  the  American  standards.  Duties  are  not  computed  on  fractions 
of  a  unit  of  measure.  Fractions  less  than  J  are  dropped ;  ^  or 
larger  fractions  are  considered  as  an  additional  unit. 

Example.  The  tariff  rate  on  macaroni  is  1  cent  per  pound. 
What  is  the  amount  of  the  duty  on  a  shipment  of  200  kilos  of 
macaroni  ? 

Solution.     1  kilo  =  2.2046  lb. 

200  kilos  =  440.92  lb.,  or  441  lb. 

Duty  on  441  lb.  at  1  cent  per  pound  is  $4.41. 

311.  Ad  Valorem  and  Specific  Duties.  In  some  cases  both  an  ad 
valorem  and  a  specific  duty  are  levied  on  the  same  importation  of 
merchandise. 

Example.  The  duty  on  perfumery  containing  alcohol  is  40 
cents  a  pound  and  60  %  ad  valorem.  What  is  the  amount  of  the 
tariff  tax  on  an  importation  of  10  kilos  of  perfumery  valued  at  970 
francs  ? 

Solution.    10  kilos  =  22.046  lb.,  or  22  lb. 

$  .40  duty  per  pound 

22  number  of  pounds 

$  8.80  specific  duty 


360  CUSTOMS  DUTIES 

1  franc  =  $  .193 
$.193  X  970  =  $  187.21  value  of  perfumery 
60  %  of  $  187  =  $  112.20  ad  valorem  duty 
$     8.80  specific  duty 

112.20  ad  valorem  duty 
1121.00  total  duty 

312.  The  Tariff.  Congress  revises  the  tariff  law  at  various 
intervals.  The  law  prescribes  the  tariffs,  or  rates,  to  be  charged 
on  various  imports.  The  free  list  comprises  those  articles  on 
which  no  duty  is  placed. 

The  following  are  some  of  the  customs  duties  from  a  recent 
tariff". 

Artificial  flowers,  60  %  ad  valorem 

Cabbage  seed,  6  cents  per  pound 

Castile  soap,  10  %  ad  valorem 

Cheese,  20  %  ad  valorem 

Cigars,  $  4.50  per  pound,  and  25  %  ad  valorem 

Cocoa,  unsweetened,  8  %  ad  valorem 

Cotton  batting,  25  %  ad  valorem 

Lithographed  booklets,  7  cents  per  pound 

Oriental  rugs,  50  %  ad  valorem 

Poppyseed,  15  cents  per  bushel 

Silk  ribbons,  45  %  ad  valorem 

Toys,  35%  ad  valorem 

Tulip  bulbs,  i  1.00  per  thousand 

Woolen  dress  goods,  35%  ad  valorem 

Written  Work 

Refer  to  the  tariff  rates  above,  and  compute  the  duty  on  the 
following  importations  of  merchandise. 

1.  50,000  tulip  bulbs  from  Holland. 

2.  Woolen  dress  goods  from  England,  valued  at  125  pounds 
sterling. 

3.  Castile  soap  from  Italy,  valued  at  40  liras. 

4.  An  invoice  of  cotton  batting  valued  at  £  20  158.  Qd. 

5.  Lithographed  booklets,  weight  247  lb.  9  oz. 


CUSTOMS  DUTIES  361 

6.  A  shipment  of  cheese  valued  at  820  marks. 

7.  Silk  ribbons  from  Paris,  invoiced  at  5400  francs. 

8.  Toys  from  Germany,  valued  at  1000  marks. 

9.  An  invoice  of  3000  cigars  from  Germany.  The  cigars 
weigh  12|  ounces  per  hundred,  and  are  invoiced  at  52  marks  per 
thousand. 

10.  The  tariff  rate  on  Cuban  cigars  is  20  %  less  than  the  rate 
applying  to  cigars  shipped  from  other  countries.  What  is  the 
duty  on  a  shipment  of  7  cases,  each  containing  3000  cigars,  weight 
14|  oz.  per  hundred;  value,  f  50.00  per  thousand? 


BUSINESS   ORGANIZATION 

CHAPTER   XXXVIII 
INDIVIDUAL  PROPRIETORSHIP 

Business  enterprises  are  usually  organized  in  one  of  the  follow- 
ing ways : 

Individual  Proprietorship.  Partnership.  Corporation. 

313.  Terms  Employed.  The  propertj^  owned  by,  and  the  debts 
owed  to,  a  business  are  its  Resources,  or  Assets. 

The  debts  owed  by  a  business  are  its  Liabilities. 

When  the  resources  exceed  the  liabilities,  the  difference  is  called 
the  Net  Worth,  Net  Capital,  or  Net  Resources. 

When  the  liabilities  exceed  the  resources,  the  difference  is 
called  the  Net  Insolvency. 

314.  Statement  of  Resources  and  Liabilities.  The  net  worth, 
or  the  net  insolvency,  of  a  business  is  shown  by  a  Statement  of 
Resources  and  Liabilities.  The  following  is  a  statement  of  the 
financial  condition  of  the  business  owned  by  J.  W.  Waterbury. 

J.  W.  Waterbury 

Statement  of  Resources  and  Liabilities 

June  30,  1917 


Resources 


Cash 

Real  Estate 
Merchandise 
James  Fitch 
F.  G.  Beach 

Total  Resources 


Balance  on  hand 
Store  and  lot 
Inventory 
Owes  the  business 
Owes  the  business 


Liabilities 
T.  E.  Madison  Business  owes  him 

Henry  Marsden  Business  owes  him 

Total  Liabilities 
J.  W.  Waterbury's  net  worth 


3500 

7500 

6325 

110 

65 


123 

962 


XX 


362 


INDIVIDUAL  PROPRIETORSHIP  363 

What  are  the  total  resources? 
What  are  the  total  liabilities? 
What  is  the  net  worth  of  the  business? 

315.  Notes  Receivable  and  Notes  Payable.  Notes  Receivable  in- 
clude such  written  obligations  as  promissory  notes,  and  acceptances, 
payable  to  the  business.  Their  number  and  value  are  shown  by 
the  record  in  the  Notes  Receivable  Book.  Notes  Payable  include 
such  written  obligations  as  promissory  notes,  and  acceptances, 
payable  by  the  business.  Their  number  and  value  are  shown  by 
the  record  in  the  Notes  Payable  Book. 

Computing  the  Interest  or  Discount  on  Notes  Receivable  and  Notes 
Payable.  Interest-bearing  Notes  Receivable  and  Notes  Payable 
are  worth  their  face  plus  accrued  interest.  The  accrued  interest 
should  therefore  be  included  in  the  statement  of  resources  and 
liabilities.  The  accrued  interest  is  the  interest  on  the  principal  for 
the  expired  time. 

Example.  J.  C.  Banner  is  making  a  statement  of  resources  and 
liabilities  on  December  31,  1917. 

Among  his  resources  is  a  note  for  $600.00,  made  by  I.  M.  Hen- 
derson, on  December  1,  1917,  due  in  90  days,  with  interest  at  6%. 
Thirty  days  have  expired  since  the  note  was  made,  and  thirty 
days'  interest  has  therefore  accrued.  The  amount  of  this  interest, 
$3.00,  being  an  obligation  payable  to  the  business,  should  be 
entered  among  the  resources. 

Among  his  liabilities  is  a  note  for  $500.00,  made  by  him  on 
December  16,  payable  in  two  months,  with  interest  at  6%.  Fif- 
teen days'  interest  has  accrued  on  this  note.  The  amount  of  the 
accrued  interest,  $1.25,  being  an  obligation  payable  5y  the  business, 
should  be  entered  among  the  liabilities. 

Non-interest-bearing  Notes  Receivable  and  Notes  Payable  are 
worth,  on  any  day,  their  face  value,  minus  the  discount  from  that 
day  until  the  day  of  maturity.     Therefore  : 

Non-interest-bearing  Notes  Receivable  should  be  entered  at 
their  face  value  among  the  resources,  and  the  amount  of  the  dis- 
count should  be  entered  among  the  liabilities. 

Non-interest-bearing  Notes  Payable  should  be  entered  at  their 


364 


INDIVIDUAL  PROPRIETORSHIP 


face  value  among  the  liabilities,  and  the  discount  should  be  entered 
among  the  resources. 

Written  Work 

1.    Complete  the  following  : 

Henry  Peterman 

Statement  of  Resources  and  Liabilities 

June  30,  1917 


Resources 

Cash 

On  hand 

2365.90 

Merchandise 

Inventory 

8926.95 

Notes  Receivable 

A.  B.  Hines's  note 

400.00 

Notes  Receivable 

H.  E.  Benton's  note 

975.00 

Interest 

24  days'  accrued  on 
Benton's  note 

? 

Discount 

15  days'  discount  on  note 
favor  of  Row 

? 

Smith  &  Edwards           Owe  the  business 
Total  Resources 

825.19 

xxxx.xx 

Liabilities 

Notes  Payable 

My  note  favor  E.  A  Clark 

360.00 

Notes  Payahle 

My  note  favor  A.  B.  Row 

420.00 

Interest 

12  days'  accrued  on  note 
favor  of  Clark 

? 

Discount 

25  days'  discount  on  A.  B. 
Hines's  note 

? 

William  Davis                Business  owes  him 
Total  Liabilities 
Henry  Peterman's  Net  Capital 

38.26 

XXX. XX 

xxxx.xx 

Explanation  of  Notes  Receivable  and  Notes  Payable.  A.  B. 
Hines's  note  was  dated  June  25,  due  in  30  days,  without  interest. 
It  was,  therefore,  due  on  July  25,  and  was  worth  its  face  minus 
25  days'  discount. 

H.  E.  Benton's  note  was  dated  June  6,  payable  in  3  months, 
with  interest  at  6  %.     24  days'  interest  accrued  since  June  6. 

Peterman's  note  in  favor  of  Clark  was  made  on  June  18,  with 
interest  at  6  %.     12  days'  interest  accrued  on  this  note. 


INDIVIDUAL  PROPRIETORSHIP  365 

Peterman's  note  in  favor  of  Row  was  drawn  on  May  15,  payable 
in  2  months,  without  interest.  It  was  due  on  July  15,  or  15  days 
from  the  day  the  statement  was  made.  Fifteen  days'  discount 
must  therefore  be  computed  on  this  note. 

Written  Work 

1.  Prepare  Statements  of  Resources  and  Liabilities  from  the 
following  facts ; 

Facts  for  statement  of  the  financial  condition  of  O.  E.  Benton, 
December  31,  1917. 

Cash,  84624.27  ;  merchandise  inventoried  at  112,417.95 ;  value 
of  store  and  lot,  ^5000.00 ;  furniture  and  fixtures  valued  at  ^420.00 ; 
delivery  equipment,  estimated  value  1270.00. 

Personal  Accounts 

F.  E.  Fairchild  owes  the  business  $215.20. 
George  Finch  owes  the  business  $28.45. 
Edgar  Knight  owes  the  business  $103.25. 
Business  owes  Justin  &  Co.  $856.75. 
Business  owes  F.  R.  Rickert  $49.00. 

Notes  and  Acceptances 

On  October  27, 1917,  Benton  gave  a  note  to  Eldridge  &  Peabody 
for  $300.00.  The  note  is  due  in  4  months,  and  bears  interest 
at  6%. 

Compute  interest  for  exact  number  of  days. 

On  December  26, 1917,  Benton  accepted  a  draft  payable  30  days 
after  sight,  for  $85.00,  without  interest,  in  favor  of  S.  B.  Gridley. 

316.   The  Profit  and  Loss  Statement. 

Gains  —  Losses  =  Net  Gain. 
Losses  —  Gains  =  Net  Loss. 

The  statement  showing  Net  Gain  or  Net  Loss  is  called  the 
Profit  and  Loss  Statement. 


366 


INDIVIDUAL  PROPRIETORSHIP 


D.  L.  Bailey 

Profit  and  Loss  Statement,  Month  Ending  October  31,  1917 


Gains 

Net  Sales  during  October 

6210.72 

Merchandise  inventory,  Oct.  1,  1917 

1233.60 

Purchases,  October 
Total 

4394.80 

5628.40 

Less  inventory,  October  31, 1917 
Cost  of  goods  sold  during  October 
Gross  trading  profit 

975.62 

4652.78 

1557.94 

Interest            On  money  loaned 

35.60 

On  money  borrowed 
Total  Gains 

6.92 

28.68 

1586.62 

Losses  and  Expenses 

Rent 

175.00 

Salaries 

460.00 

Advertising 

56.20 

Heat  and  light 

32.00 

Delivery  charges 

56.35 

Insurance  and  taxes 

73.85 

General  expense 

92.74 

Depreciation 

70.00 

Loss  from  bad  debts 

Total  losses  and  expenses 
Net  Gain 

15.75 

1031.89 

554.73 

Written  Work 

1.  Percentage  Analysis  of  Profit  and  Loss  Statement. 
Answer  the  following  questions  : 

The  net  profit  shown  by  the  above  statement  is  what  per  cent 
of  the  net  sales  ? 

Each  of  the  losses  or  expenses  is  what  per  cent  of  the  net 
sales  ? 

2.  Prepare  a  Profit  and  Loss  Statement  and  a  Percentage  Anal- 
ysis from  the  following  facts : 

Statement  for  the  year  1917,  made  December  31,  1917.  Busi- 
ness owned  by  Oscar  Clark. 


INDIVIDUAL  PROPRIETORSHIP  367 

Net  Sales,  1917,  $26,746.27. 
Purchases,  1917,  f  22,860.39. 
Inventory,  December  31,  1916,  f  4,219.26. 
Inventory,  December  31,  1917,  15,126.99. 

Interest : 

6  months'  accrued  interest  at  6  %  on  Clark's  note  of  $  345.00  in 
favor  of  Jenkins. 

30  days'  accrued  interest  at  5  %  on  Clark's  note  of  f  280.00  in 
favor  of  Michelson. 

2  months'  accrued  interest  on  Bailey's  note  in  favor  of  Clark. 
Face  of  note,  I  375.00;  rate,  6  %. 

28  days'  interest  has  accrued  on  a  note  given  by  Snyder  to 
Clark  on  December  3,  1917.     Face  of  note,  I  240.00  ;  rate,  6  %. 

An  extra  salesroom  was  rented  for  the  year  at  a  monthly  rental 
of  $  20.00. 

Salaries  : 

Clerk,  12  months  at  $  35.00  per  month. 

Delivery  boy,    3  months  at  $  15.00  per  month ; 
9  months  at  $  16.00  per  month. 

Heat  and  light,  1119.25. 

Feed  and  care  of  delivery  horse,  $64.00. 

Value  of  store  building,  8  3000.00  ;  value  of  lot,  $  800.00. 

Store  and  lot  assessed  at  J  of  its  value  and  taxed  at  a  rate  of 
12.16. 

Stock  valued  at  $4000.00  ;  assessed  at  ^  of  its  value  and  taxed 
at  a  rate  of  $2.16. 

An  insurance  policy  was  carried  on  the  store  and  one  on  the 
stock. 

Store  insured  at  80  %  of  its  value  ;  rate,  $  1.15. 

Stock  insured  under  a  policy  of  $  3000.00 ;  rate,  81.15. 

Annual  depreciation  on  store  building  charged  at  3  %. 

Loss  from  bad  debts  estimated  at  |  %  of  gross  sales. 

General  expense,  $  114.17. 


CHAPTER   XXXIX 

PARTNERSHIP 

"A  partnership  or  firm  is  an  association  composed  of  two  or 
more  persons,  formed  for  the  purpose  of  carrying  on,  as  co-owners, 
a  business  with  a  view  to  profit."  *  Partners  are  liable  individ- 
ually for  the  debts  of  the  partnership  which  cannot  be  paid  from 
the  resources  of  the  partnership. 

317.  Sharing  Profits  and  Losses  Equally.  When  partners  make 
equal  investments  and  contribute  equal  values  of  skill  and  service, 
it  is  customary  to  divide  gains  and  losses  equally.  If  the  partner- 
ship contract  does  not  specify  the  ratio  in  which  profits  and 
losses  are  to  be  shared,  the  law  provides  that  they  shall  be  shared 
equally. 

Written  Work 

1.  Oldham,  Barnes  &  Snowden  each  invests  $4000  in  a  partner- 
ship, the  gains  and  losses  of  which  are  to  be  shared  equally.  The 
following  statements  show  the  distribution  of  the  net  gain.  Com- 
plete the  statements. 

Oldham,  Barnes  &  Snowden 
Profit  and  Loss  Statement  for  the.  Year  Ending  December  31,  1917 


Gains 
Mdse.  Sales  18,226.55 

Mdse.  Purchases  17,847.90 

Mdse.  Inventory  Dec.  31,  '17    3,472.00 
Cost  of  goods  sold  xx,xxx.xx 

Mdse.  Gain  (gross  trading  profit) 
Purchase  Discounts 
Sales  Discounts 
Gain 

Total  Gains 


135.85 

57.80 


Expense 
Interest 
Interest 

Total  Losses 
Net  Gain 


Losses 

For  the  year 

On  borrowed  funds 

On  money  loaned 

For  the  year 


28.35 
3.50 


xxxx.xx 
xx.xx 


1245.25 
xx.xx 


*  Sec.  8  of  Draft  of  an  Act  to  make  uniform  the  Law  of  Partnership. 

368 


PARTNERSHIP 


369 


Oldham,  Barnes  &  Snowden 

Statement  of  Distribution  of  Profit 

Year  Ending  December  31,  1917 


Investment  4000.00 
1  net  gain        xxx.xx 

Total  xxxx.xx 

Withdrawals    150.00 

Net  worth 

Investment  4000.00 
\  net  gain  xxx.xx 
Total  xxxx.xx 

Withdrawals    125.00 

Net  worth 

Investment  4000.00 
i  net  gain        xxx.xx 

Total  xxxx.xx 

Withdrawals    160.00 
Net  worth 
Oldham,  Barnes  &  Snowden,  Net  worth 


G.  F.  Oldham 


D.  M.  Barnes 


Wm.  A.  Snowden, 


xxxx.xx 


Oldham,  Barnes  &  Snowden 

Statement  of  Resources  &  Liabilities 

December  31,  1917 


Resources 
Cash  On  hand 

Merchandise  Inventory 

Accounts  Receivable  Per  schedule 
Notes  Receivable  Per  notebook 
Interest  Accrued  on  Notes  Receivable 

Total  Resources 


Accounts  Payable 
Notes  Pavable 


Liabilities 

Per  schedule 
Per  notebook 


Total  Liabilities 
Net  Capital 
Divided  as  follows : 
G.  F.  Oldham 
D.  M.  Barnes 
Wm.  A.  Snowden 
Total  (as  above) 


Of  the  partnership 


3240.90 

9872.35 

3132.35 

275.00 

3.50 


1800.50 
500.00 


xxxx.xx 
xxxx.xx 
xxxx.xx 


xxxx.xx 


xxxx.xx 


xxxx.xx 


xxxx.xx 


370  PARTNERSHIP 

2.    Prepare  completed  copies  of  the  following  statements 

Wadhams  &  Lee 
Financial  Statement 

December  31,  1917 


Besources 
Cash                             On  hand 
Merchandise                 Inventory 
Real  Estate                  Store  and  lot 
Notes  Receivable        Per  notebook 
Interest                         Accrued  on  notes  receivable 
Accounts  Receivable  Per  schedule 
Total  Resources 

Liabilities 
Notes  Payable              Per  notebook 
Interest                         Accrued  on  notes  payable 
Accounts  Payable       Per  schedule 
Total  Liabilities 
Net  Capital 

246.90 
5724.60 
4195.00 
1600.00 
8.00 
2640.35 

2000.00 

12.50 

1347.28 

XX,  XXX. XX 

x,xxx.xx 

XX,  XXX. XX 

Wadhams  &  Lee 

Statement  of  Profits  and  Losses 

Year  Ending  December  31,  1917 


Taxes 


Insurance 


Losses 

On  store  and  lot 
On  stock 

On  store 
On  stock 


Interest  Accrued  on  notes  payable 

Accrued  on  notes  receivable 

Sales  Discounts 
Purchase  Discounts 
General  Expense 
Total  Losses 

Gains 
Merchandise  Sales 
Merchandise  In  v.  1/1/' 17 
Merchandise  Purchase 
Cost  of  Merchandise 
Inventory  12/31/'  17 
Cost  of  Goods  Sold 
Gross  Earnings 
Net  Loss 


32.00 
24.00 

48.00 
32.00 

12.50 
8.00 

86.40 
69.25 


3,000.00 

12,416.20 

xx,xxx.xx 

x,xxx.xx 


XX.  XX 

1378.90 


11,147.80 


X.XXX.XX 


x,xxx.xx 


PARTNERSHIP 


371 


Wadhams  &  Lee 
Capital  Accounts 


James  Wadhams 


Net  Capital 
Edwin  C.  Lee 


Investment 
Withdrawals 
Net  Investment 
^  Net  Loss 

Investment 
Withdrawals 
Net  Investment 

^  Net  Loss 


6000.00 

426.93 

xxxx.xx 

XX.  XX 


6000.00 

340.70 

xxxx.xx 

XX.  XX 


Net  Capital 
Wadhams  &  Lee,  Net  Capital 


318.  Sharing  Profits  and  Losses  According  to  Arbitrary  Propor- 
tion. When  partners  contribute  unequal  amounts  of  time  or  skill, 
they  frequently  divide  the  profits  in  some  arbitrary  proportion. 

Written  Work 

1.  Davis,  a  lawyer,  admits  two  younger  lawyers,  Fritz  and 
Healy,  into  partnership.  Since  Davis  has  an  established  practice, 
it  is  agreed  that  he  shall  receive  f  of  the  net  earnings,  and  that 
Fritz  and  Healy  shall  divide  the  remainder  equally. 

The  net  earnings  the  first  year  are  iSOOO  ;  the  second  year  they 
are  ^9260.     Compute  the  division  of  the  profits  each  year. 

319.  Sharing    Profits    and    Losses    According    to    Investments. 

When  partners  contribute  unequal  amounts  of  capital,  gains  or 
losses  are  often  shared  in  proportion  to  the  capital  invested. 

Example.  Nelson  invested  $2000,  Baker  $3000,  and  Ander- 
/?on  $5000  in  a  business  which  gained  $1256.70.  What  was 
each  partner's  share  of  the  gain  ? 

Solution. 

Partners  Investment 


Proportion  op 
Investment 


Share  of 
Oains  or  Losses 


TSoSo 


Nelson  ^2000 

Baker  $3000 

Anderson  $5000 

The  gain  for  the  year  was  $1256.70. 

\  of  $1256.70  =  $251.34,  Nelson's  share. 
j\  of  $  1256.70  =  $377.01,  Baker's  share. 
I  of  $  1256.70  =  $  628.35,  Anderson's  share. 


372 


PARTNERSHIP 


Written  Work 

1.  A  invests  $4500.  B  invests  16000.  C  invests  $7500. 
Profits  and  losses  are  to  be  shared  in  proportion  to  investment. 
The  first  year  there  was  a  gain  of  $2461.25.  What  was  the 
amount  of  profit  received  by  each  partner  ? 

2.  On  July  1,  1918,  D.  M.  Paine,  F.  R.  Adamson,  and  B.  O. 
Cone  entered  into  partnership.  Gains  and  losses  were  to  be  shared 
in  proportion  to  investment. 

Paine,  who- had  been  conducting  a  grocery  business,  turned  into 
the  partnership  his  entire  resources  and  liabilities,  as  shown  by 
the  following  statement  : 

D.  M.  Paine 

Statement  of  Resources  and  Liabilities 

July  1,  1918 


Resources 
Cash  On  hand 

Merchandise  Per  inventory 

Real  Estate  Store  and  lot 

Furniture  and  Fixtures 
Accounts  Receivable       Per  ledger 
Total 

Liabilities 
Accounts  Payable  Per  ledger 


Notes  Payable 
Interest 

Total 
Net  Capital 


Per  bill  book 

Accrued  on  notes  payable 

D.  M.  Paine 


316.75 
4135.60 
3000.00 

350.00 
1237.80 


xxxx.xx 


He  gave  his  note  with  interest  at  6  %,  dated  July  1,  1918, 
payable  to  Paine,  Adamson  &  Cone,  for  an  amount  sufficient  to 
make  his  total  investment  $8000. 

Adamson  invested  the  following  : 

Merchandise,  $  1200. 

A  note  in  his  favor,  signed  by  O.  G.  Dunlap,  for  $2500, 
dated  April  1,  1918,  due  iu  1  year,  bearing  6  %  interest.  (Is  this 
note  worth  its  face,  its  face  plus  accrued  interest,  or  its  face 
minus  the  discount  until  maturity  ?) 


PARTNERSHIP 


373 


Cash  to  make  his  total  investment  i  4000. 

Cone  invested  a  draft  for  $  740,  drawn  by  himself  on  Graf  & 
Knight,  on  June  18,  1918,  payable  30  days  after  sight,  without 
interest.  Graf  &  Knight  accepted  the  draft  on  June  20,  1918. 
Cone  also  invested  enough  cash  to  make  a  total  investment  of 
$  3000. 

Prepare  a  statement  of  resources  and  liabilities,  showing  the 
net  capital  of  the  firm  of  Paine,  Adamson  &  Cone,  at  the  begin- 
ning of  business  on  July  1,  1918.  The  following  illustration  will 
show  the  form  of  the  statement : 

Paine,  Adamson  &  Cone 
Statement  of  Resources  and  Liabilities,  July  1,  1918 


Cash 


Resources 

Invested  by  Paine  xxx.xx 

Invested  by  Adamson  xxx.xx 
Invested  by  Cone         xxxx.xx 


Merchandise  Invested  by  Paine       xxxx.xx 

Invested  by  Adamson  xxxx. 
Real  Estate 

Furniture  and  Fixtures 
Notes  Receivable    Paine's  note  favor 

P.  A.  &  C.  xxx.xx 

Dunlap's  note  favor 

Adamson  xxxx. 

Cone's  draft  on 

G.  &  K.  XXX. 

Interest  Accrued  on  Dunlap's 

note 
Accounts  Receivable  from  Paine 
Total 

Liabilities 

Received  from  Paine 
Accrued  on  note  rec'd 

from  Paine  x.xx 

Discount  on  Cone's 

draft  

Accounts  Payable  Received  from  Paine 
Total 
Net  Capital        Paine,  Adamson  &  Cone 


Notes  Payable 
Interest 


x.xx 


xxxx.xx 


xxxx.xx 
xxxx. 

XXX. 


XX.XX 

xxxx.xx 


X.XX 

xxx.xx 


xx.xxx.xx 


x,xxx.xx 


xx,xxx. 


374 


PARTNERSHIP 


What  fraction  of  the  net  gains  should  each  partner  receive  if 
gain  is  shared  in  proportion  to  capital  invested  ? 

On  December  31,  1918,  a  statement  of  resources  and  liabilities 
of  the  firm  showed  the  following  facts  : 

Statement  of  Resources  and  Liabilities 
Paine,  Adamson  &  Cone 

December  31,  1918 


Resources 
Cash  On  hand 

Merchandise  Inventory 

Real  Estate 

Furniture  and  Fixtures 
Accounts  Receivable 
Total 

Liabilities 
Accounts  Payable 
Total 
Net  Capital  Paine,  Adamson  &  Cone 


2,215.60 

15,465.70 

2,910.00 

339  50 

4,285.37 


1941.20 


xx,xxx.xx 


x,xxx.xx 


xx,xxx.xx 


What  was  the  increase  in  the  capital  of  the  business  during  the 
6  months'  period  ? 

This  increase  represents  the  profits  remaining  in  the  business. 
During  the  6  months'  period,  the  partners  withdrew  profits  as 
follows : 


Partner 

Amount 

Paine 

Adamson 

Cone 

11413.32 
1206.66 
1654.99 

$4274.97 

What  was  the  total  gain  for  the  6  months'  period  ? 

What  share  of  the  gain  was  each  partner  entitled  to  receive  ? 

Each  partner  has  already  drawn  out  a  portion  of  his  profits. 
How  much  is  he  still  entitled  to  receive  ? 

The  partners  decide  to  add  the  remainder  of  their  profits  to 
their  investments.  What  was  the  investment  of  each  partner  on 
January  1,  1919  ? 


PARTNERSHIP 


375 


Prepare  a  Statement  of  Distribution  of  Profit  similar  to  the 
model  on  page  369,  showing  the  original  investment,  gains,  with- 
drawals, and  net  worth  of  each  partner  as  of  June  30,  1919. 

On  the  basis  of  this  investment  what  fractional  part  of  the 
profits  of  1919  should  each  partner  receive  ? 

On  June  30,  1919,  a  statement  of  resources  and  liabilities 
showed  the  following  facts  : 

Statement  of  Resources  and  Liabilities 

Paine,  Adamson  &  Cone 

June  30,  1919 


Resources 
Cash  On  hand 

Merchandise  Inventory- 

Real  Estate 

Furniture  and  Fixtures 
Accounts  Receivable  Per  ledger 
Total 

Liabilities 
Accounts  Payable        Per  ledger 
Notes  Payable  Per  bill  book 

Interest  Accrued  on  notes  payable 

Total 
Net  Capital  Paine,  Adamson  &  Cone 


1846.03 
8420.50 
2820.00 
329.00 
5627.38 


1240.65 

1000.00 

13.33 


xx,xxx.xx 


x,xxx.xx 


xx,xxx.xx 


What  was  the  net  gain  or  net  loss  for  the  6  months'  period  ? 

Prepare  a  statement  showing  the  investment  of  each  partner  on 
January  1,  1919,  the  distribution  of  gain  or  loss,  and  the  invest- 
ment of  each  as  of  June  30, 1919. 

320.    Computing  Interest  on  Investments  and  Withdrawals.     It 

is  sometimes  agreed  that  each  partner  shall  receive  interest  on 
his  investment,  and  that  after  this  interest  has  been  paid,  or 
credited,  to  the  partner,  the  remaining  profits  shall  be  divided 
according  to  agreement. 

Example.  At  the  beginning  of  the  year  Briggs  invests 
$8000.00  and  Duncan  invests  17500.00.  It  is  agreed  that  each 
partner  shall  receive  6  %  interest  on  his  investment,  payable  out 
of  the  profits,  and  that  the  remaining  profits  shall   be   divided 


376 


PARTNERSHIP 


equall3^     The  net  gain  for  the  year  is  $2800.00.     What  interest 
and  what  share  of  the  remaining  gain  does  each  partner  receive  ? 
Solution.     6  %  interest  for  1  year  on  1 8000  =  f  480,  Briggs's  interest. 
6  %  interest  for  1  year  on  <|  7500  =  $  450,  Duncan's  interest. 
$  2800     Net  gain 

930     Total  interest 
«f  1870     Remaining  profits 
$  1870  -^  2  ==  $  935.     Share  of  profit  for  each  partner 
Briggs's  total  interest  and  gain,  $  480  +  $  935  =  1 1415. 
Duncan's  total  interest  and  gain,  $450  +  $935  =  $1385. 

Written  Work 

1.  Jones  and  Morgan  began  a  partnership  July  1,  1917;  Jones 
invested  $9500.00  and  Morgan  invested  $11,500.00.  Each 
partner  was  to  receive  interest  on  his  investment  at  the  rate  of 
5  %  per  year,  the  remaining  net  profit  or  loss  to  be  divided  equally. 
On  December  31,  1917,  a  statement  of  the  losses  and  gains  of  the 
firm  showed  a  net  gain  of  $815.00.  What  amount  of  interest 
and  remaining  profit  should  each  partner  have  received? 

2.  Wallace  and  Montgomery  entered  into  partnership  on  Janu- 
ary 1,  1917.  Each  of  these  men  had  formerly  conducted  a  busi- 
ness of  his  own,  and  each  turned  into  the  partnership  his  entire 
resources  and  liabilities,  as  shown  by  the  following  statements : 

L.  F.  Montgomery 
Statement  of  Resources  and  Liabilities,  December  31,  1916 


1 

Resources 
Cash                                  On  hand 
Merchandise                     Per  inventory 
Real  Estate                       Store  and  lot 
Fixtures                            Per  inventory 
Accounts  Receivable       Per  schedule 
Interest                              Discount  on  notes 
Total 

Liabilities 
Accounts  Payable            Per  schedule 
Notes  Payable                  Per  bill  book 
Total 
Net  Investment,  L.  F.  Montgomery 

1215.75 

3565.80 

3000.00 

419.75 

625.90 

4.18 

1275.90 
1418.00 

xxxx.xx 

xxxx.xx 

xxxx.xx 

PARTNERSHIP 


377 


Irving  Wallace 
Statement  of  Resources  and  Liabilities,  December  31,  1916 


Resources 


Cash 

Merchandise 
Fixtures 

Accounts  Receivable 
Total  Resources 


On  hand 
Per  inventory 

Per  ledger 


Liabilities 
Accounts  Payable  Per  ledger 


Total  Liabilities 
Net  Investment 


Irving  Wallace 


x,xxx.xx 


x,xxx.xx 


x,xxx.xx 


It  is  agreed  that  each  of  the  partners  shall  receive  interest  on 
his  investment  at  the  rate  of  6  %  per  annum,  remaining  profit  to 
be  divided  equally. 

On  December  31,  1917,  the  following  statement  showed  the 
condition  of  the  firm  : 

Wallace  and  Montgomery 

Statement  of  Resources  and  Liabilities 

December  31,  1917 


Resou 
Cash 

Merchandise 
Real  Estate 
Fixtures 

Accounts  Receivable 
Interest 

rces 

On  hand 
Per  inventory 
Store  and  lot 
Per  schedule 
Per  schedule 
Discount  on  notes 

ities 

Per  schedule 
.  Per  bill  book 

ce  and  Montgomery 

1462.80 
7292.90 
3000.00 
632.86 
1853.27 
2.09 

Total 

Liahil 
Accounts  Payable 
Notes  Payable 

615.20 
1418.00 

XXjXXX.XX 

Total 

x,xxx.xx 

Net  .Capital,  Walla 

xx,xxx.xx 

What  amount  of  interest  should  each  of  the  partners  receive  ? 

After  paying  interest  out  of  profits,  what  amount  of  profit  re- 
mains, and  what  share  of  this  profit  should  each  partner  receive  ? 
No  withdrawals  were  made  by  either  partner. 


CHAPTER   XL 
INSOLVENCY  AND  BANKRUPTCY 

Individuals,  firms,  or  corporations  which  are  not  able  to  pay 
'their  debts  when  due,  or  whose  liabilities  exceed  their  resources, 
are  said  to  be  insolvent.  Under  the  Federal  law,  any  person 
in  a  condition  of  insolvency  may  be  declared  a  bankrupt  if  he  so 
desires.  His  resources,  frequently  called  assets,  with  the  exception 
of  certain  exempt  property,  are  turned  over  to  a  Trustee  repre- 
senting the  creditors,  and  divided  proportionately  among  them,  all 
creditors  except  those  whose  claims  are  preferred  or  secured  re- 
ceiving the  same  fractional  part  or  per  cent  of  the  amount  due 
them. 

321.  Bankruptcy  Proceedings.  The  creditors  of  any  insolvent 
person  except  a  "  wage-earner  "  earning  less  than  f  1500  per  year, 
or  a  "person  engaged  chiefly  in  farming  or  tillage  of  the  soil," 
may  institute  bankruptcy  proceedings  against  him,  if  he  has  done 
one  of  the  following  acts  : 

a.  Transferred  or  concealed  any  of  his  property  with  intent  to 
delay  payment  or  to  defraud  his  creditors. 

h.  Transferred  property  to  one  creditor  for  the  purpose  of  giv- 
ing him  an  advantage  over  the  other  creditors. 

c.  Allowed  one  creditor  to  obtain  a  preference  through  legal 
proceedings. 

d.  Made  an  assignment  of  all  his  property  to  a  trustee  for 
creditors. 

e.  Admitted  in  writing  his  inability  to  pay  his  debts,  and  his 
willingness  to  be  adjudged  a  bankrupt. 

After  a  debtor  has  "  gone  into  bankruptcy  "  and  made  a  settle- 
ment by  turning  over  his  assets,  he  is  legally  discharged  from  his 
indebtedness.  Any  resources  which  he  may  possess  at  a  later 
time  cannot  be  taken  in  further  payment  of  debts  settled  in 
bankruptcy. 

378 


INSOLVENCY  AND  BANKRUPTCY  379 

Illustration  of  a  Settlement  in  Bankruptcy.  On  October  20, 
1917,  J.  D.  Marphy  was  declared  a  bankrupt,  and  a  trustee  was 
elected  by  the  creditors  to  take  over  his  assets,  convert  them  into 
cash,  and  pay  the  creditors.  Mr.  Murphy  filed  the  following 
schedule  of  assets  and  liabilities  at  book  values : 


Schedule 

OF  Assets  &  Lia 
Assets 

BILITIES 

Cash 

$   465.00 

Merchandise 

3225.00 

Real  estate 

8500.00 

Accounts  receivable 

Liabilities 

3688.18 

$15,878.18 

Taxes 

$   165.00 

Wages 

233.00 

Mortgage  on  real  estate 

2000.00 

Hartman,  Oelberg  &  Co. 

2146.80 

D.  G.  Barnhard 

364.00 

Franklin  &  Gertz 

7685.25 

D.  0.  Mitchell 

8146.30 

$20,740.35 

The  trustee  sold  the  real  estate  to  the  holder  of  the  mortgage 
for  $5800  in  excess  of  the  mortgage.    • 
Cash  receipts  were  as  follows  : 

From  Murphy  $   465.00 
From  the  sale  of  the  real  estate  after  paying 

the  mortgage  5800.00 

From  the  sale  of  merchandise  2900.00 

From  accounts  receivable  collected  3500.00     $12,665.00 

He  made  payments  as  follows: 

Wages    (which   are  a  preferred  claim   and 

must  be  paid  before  the  other  liabilities)  $  233.00 

Taxes  (which  are  also  a  preferred  claim)  165.00 

His  fee  as  receiver,  allowed  by  court  250.00     $      648.00 

Balance  of  cash  on  hand  $12,017.00 

The  unpaid  liabilities  are  as  follows  : 

Hartman,  Oelberg  &  Co.  $2146.80  ^ 

D.  G.  Barnhard  '  364.00 

Franklin  &  Gertz  7685.25 

D.O.Mitchell  8146.30    $18,342.35 


380  INSOLVENCY  AND  BANKRUPTCY 

The  receiver  will  be  able  to  pay  or  65.5  %  of  the  lia- 

18342.35 

bilities.  Each  creditor  will  receive  65.3  %  of  his  claim.  The  com- 
mon expression  of  this  settlement  is,  "  Mr.  Murphy  paid  65  cents 
on  the  dollar." 

Written  Work 

1.  On  August  25,  1917,  Fred  Helms  made  an  assignment  to  his 
creditors,  turning  over  the  following  assets  to  a  receiver : 

Cash  on  hand  and  in  bank  $     85.00 

Merchandise  inventoried  at  2300.00 

Store  property,  book  value  3500.00 

Accounts  receivable  1632.50 

His  liabilities  were  as  follows : 

Wages,  preferred  claim  $     95.00 

Accounts  payable : 

Weston  and  Burton  1036.49 

George  Seeley  &  Co.  378.57 

J.  G.  O'Shea  1275.85 

Holden  &  Plehn  5300.00 

Wm.  Meyers  3000.00 

The  receiver  is  able  to  realize  $2000  on  the  merchandise.  The 
store  property  is  old  and  no  depreciation  has  been  deducted  on  Mr. 
Helms'  books.  The  receiver  is  able  to  sell  it  for  only  §2400. 
He  collects  all  of  the  accounts  receivable  with  the  exception  of 
$212.50. 

The  receiver  pays  the  wages,  $95  ;  the  expenses  of  the  receiver- 
ship, $75,  and  his  own  fee  of  $100,  which  is  allowed  by  the  court. 
The  remaining  cash  is  distributed  among  the  creditors. 

How  much  does  each  creditor  receive? 


CHAPTER   XLI 
CORPORATIONS,  STOCKS,  AND  BONDS 

The  method  and  the  advantages  of  organizing  a  business  as  a 
corporation  may  be  shown  by  an  illustration. 

William  Austin  has  $75,000.00;  125,000.00  of  this  amount  is 
invested  in  business.  He  has  f  50,000.00  remaining,  which  he 
wishes  to  invest  in  a  factory  for  manufacturing  carriages. 

George  Fox  has  §30,000.00,  which  represents  his  entire  capital, 
and  he  is  willing  to  join  Austin  in  the  organization  of  a  carriage 
manufacturing  business. 

Austin  and  Fox  believe  that  a  capital  of  i  100,000.00  is  neces- 
sary for  the  successful  operation  of  a  business  such  as  they  wish 
to  organize,  but  together  they  are  able  to  invest  only  $80,000.00. 
In  order  to  obtain  the  remaining  $20,000.00,  they  may  take  one 
or  more  persons  into  partnership,  or  they  may  organize  a  cor- 
poration. 

322.  Partnership  and  Corporation  Contrasted.  The  disadvan- 
tages of  a  partnership     re  : 

a.  Each  partner  is  personally  liable  for  the  debts  of  the 
partnership. 

h.  Partners  frequently  have  difficulty  in  withdrawing  from  a 
partnership. 

Unless  at  the  time  of  organizing  a  partnership  a  definite  date 
is  set  when  the  partnership  may  be  dissolved,  no  partner  can 
withdraw  from  the  business  without  the  consent  of  the  other 
partners.  The  law  does  not  permit  a  partner  to  sell  his  interest  in 
the  partnership  without  the  consent  of  the  other  partners. 

c.  The  death,  bankruptcy,  or  insanity  of  a  partner  dissolves 
the  partnership. 

The  advantages  of  a  corporation  are  : 

a.  Each  member  (stockholder)  of  the  corporation  is  liable  for 
only  the  amount  he  contributes  to  the  capital  of  the  corporation. 

381 


382 


CORPORATIONS,  STOCKS,   AND  BONDS 


His   private   resources   cannot   be   taken   for   the   debts   of    the 
corporation. 

h.  Any  stockholder  may  sell  his  interest  in  the  corporation 
without  the  consent  of  the  other  stockholders,  and  without  dis- 
solving the  corporation. 

c.  The  death  or  bankruptcy  of  a  stockholder  does  not  dissolve 
a  corporation. 

d.  By  the  method  of  selling  shares  of  stock  (to  be  explained 
later)  an  individual  may  invest  a  small  amount  of  money  in  a 
large  corporation.  The  capital  of  the  railroads  and  other  large 
corporations  is  usually  furnished  by  thousands  of  stockholders. 
Partnerships  of  such  a  size  would  be  unwieldy  and  impracticable. 

Considering  these  advantages,  Austin  and  Fox  decide  to  incor- 
porate, and  after  complying  with  the  legal  requirements  they, 
prepare  a  subscription  list  on  which  to  receive  subscriptions  to 
the  capital  stock. 


^ubflfcrtjption  ilitft 
The  Eclipse  Carriage  Company 

We,  the  undersigned,  hereby  subscribe  for  the  number  of  shares  and  the  amount 
of  the  Capital  Stock  of  the  Eclipse  Carriage  Company  set  opposite  our  names,  agree- 
ing to  pay  for  the  same  on  June  1,  19 


Date 

Number  of  Shares 
Face  Value  $100.00 

Amount 
Par  Value 

Signature 

Residence 

ify 

^W..^.^^^^. 

/  <£o.o  oo 

U)^/A....r7^.^/z^:. 

/*^^^^.<rD        9yjk 

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^-^^^«^ 

O^^..^/:.^^^^^^. 

/rinnn 

^'^^^^^uc^  Jy-<r»t^ 

-^^.J^. 

V 

r^J/-.. 

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^^iUa:*«t,,  "^SlSL 

^^ 

f< 

T.  .7.  flMnA^k 

flun^mA.    n9/I 

^ 

^ 

ig^PPUu^^ 

■m>^i^««P*5'  Vi4^^ 

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^^.  ^ 

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^.^.JA/^^^^^yJ^ 

7'^r,t^:;^^zr-'3bu^t. 

^ 

CORPORATIONS,   STOCKS,   AND  BONDS 


383 


323.  Terms  Used.  The  Capital  Stock  of  a  corporation  is  the 
amount  of  capital  authorized  by  the  charter. 

Shares.  The  capital  stock  is  divided  into  shares  of  equal  size, 
having  a  nominal  or  face  value,  usually  of  i  100. 00.  Shares  may 
be  of  any  denomination  within  the  limits  fixed  by  law. 

When  the  stock  has  been  subscribed  (and,  in  some  states,  paid 
in)  a  meeting  of  the  stockholders  is  held  at  which  meeting  a 
board  of  directors  is  elected  to  manage  the  business. 

At  this  meeting  each  share  owned  by  a  stockholder  entitles 
him  to  one  vote.  (How  many  votes  should  Austin  have?)  By 
this  method  of  voting  it  is  possible  for  a  few  stockholders  own- 
ing a  majority  of  the  shares  to  control  the  business. 

324.  Stock  Certificates.  Each  stockholder  receives  a  certificate, 
signed  by  the  officers  of  the  corporation,  stating  the  number  of 
shares  for  which  he  has  subscribed  and  paid. 


Capital  Stock 

$100,000.00 


1000  Shares 
$100.00  Each 


The  Eclipse  Carriage  Company 


STOCK  CERTIFICATE 

NO.  _^£: 


Stjia  (HertififB  that 

IS  the  owner  oiS 


NUMBER  OF  SHARES 


c^rU. 


shares  of  the  Capital  Stock 


of  Qllff  &litiar  Qlama^r  (Sontfiany.  fully  paid  and  non-assessable, 
transferable?  only  on  the  books  of  the  Corporation  by  the 
holder  hereof  in  person  or  by  Attorney  upon  surrender  of  this 
Certificate  properly  endorsed 

Jn  Sitttfaa  Vifrrrof.  the  said  Corponmon  has 
caused  this  Certificate  to  be  signed  by  its  duly  authonzed 
)     c„i     (  officers,   and 

ration,  at- 

o\yt^''tcr AD.  iq/<^ 


be  sealed  with  the  Seal  of  the  Corpo- 
C^C^.    this        /  day 


M-^/--^-.(^.yr^.,_ 


'■"'^r^. 


384  CORPORATIONS,  STOCKS,  AND  BONDS 

Oral  Work 

Refer  to  the  stock  certificate,  and  answer  the  following 
questions : 

1.  What  is  the  total  capital  stock  of  the  corporation? 

2.  Into  how  many  shares  is  the  capital  stock  divided? 

3.  What  is  the  par  (face)  value  of  each  share  ? 

4.  How  many  shares  does  Robbins  own  ?  To  how  many  votes 
is  he  entitled? 

5.  What  is  the  par  value  of  his  stock? 

325.  Dividends.  The  profits  of  the  corporation  which  are 
divided  among  the  stockholders  are  called  Dividends.  The 
board  of  directors  has  the  authority  to  determine  the  amount  of 
dividends  which  shall  be  declared  out  of  the  profits. 

326.  Surplus.  The  undivided  profits  of  a  corporation  are  held 
as  surplus. 

Examples.  1.  Let  us  suppose  that  the  Eclipse  Carriage  Com- 
pany's profits  at  the  end  of  one  year  amounted  to  »$6800.  What 
per  cent  of  dividends  could  the  directors  declare  ? 

Solution.     ^  6800  (Profits)  --  1 100,000  (Capital  Stock)  =  6.8  %. 

Therefore,  the  largest  dividend  which  the  directors  could  declare  is  6.8  %. 
If  such  a  dividend  were  declared,  each  stockholder  would  receive  6.8  %  of  the 
par  value  of  his  stock. 

Austin,  owning  500  shares,  with  a  par  value  of  f  50,000,  would  receive  a  divi- 
dend of  6.8  %  of  the  par  value  of  |  50,000,  or  $3400. 

2.  Let  US  suppose  that  the  directors  vote  to  declare  a  5  %  divi- 
dend. How  much  of  the  profits  would  be  divided  among  the 
stockholders,  and  how  much  would  remain  as  surplus  ? 

Solution.     5  (fo  of  %  100,000  =  $  5000,  Total  Dividend. 

$6800  (Profits) -$5000  (Dividends)  =$1800,  Surplus. 

327.  Par  Value  and  Market  Value  of  Stock.  The  par  value  or 
nominal  value  of  stock  is  its  face  value,  shown  by  the  stock  cer- 
tificate. 

The  market  value  of  a  share  is  the  amount  for  which  it  can  be 


CORPORATIONS,  STOCKS,  AND  BONDS  385 

sold.  The  market  value  depends  upon  several  factors,  the  fol- 
lowing being  the  most  important : 

a.    The  value  of  the  property  owned  by  the  corporation. 

When  the  Eclipse  Carriage  Company  was  organized,  each  stock- 
holder paid  for  his  stock  in  cash,  and  for  each  share  of  stock  there 
was  ilOO  in  the  treasury.  Each  share,  therefore,  was  worth 
f  100.  But  let  us  assume  that  a  surplus  of  i  1600  has  been 
created.  Since  there  are  one  thousand  shares,  this  surplus  adds 
f  1.60  to  the  property  represented  by  each  share. 

h.    The  dividends  paid  by  the  corporation. 

Let  us  suppose  that  9  %  dividends  are  declared  each  year. 
$  9  is  6  %  income  on  8  150,  and  Jones  might  be  willing  to  pay 
'f  150  for  a  share  of  this  stock. 

If  only  4  %  dividends  were  paid,  Jones  would  probably  not  be 
willing  to  pay  $  100  for  a  share  because  he  would  not  receive 
6  %  on  his  investment. 

When  stock  sells  for  more  than  its  par  value,  it  is  said  to  be 
above  par,  or  at  a  premium.  Stock  selling  for  i  105  per  share  is 
quoted  at  105. 

When  stock  sells  for  less  than  its  par  value,  it  is  said  to  be  below 
par,  or  at  a  discount.     Stock  selling  for  f  95  is  quoted  at  95. 

328.  Assessments.  When  money  is  required  to  cover  losses,  or 
to  extend  the  business,  in  some  companies  the  stockholders  may 
vote  to  levy  an  assessment.  The  assessment  is  a  per  cent  of  the 
par  value  of  the  stock,  and  is  paid  by  the  stockholders  to  the  treas- 
urer of  the  corporation.     Shares  of  stock  may  be  non-assessable. 

Written  Work 

1.  The  stock  of  a  corporation  has  all  been  subscribed  and  is 
owned  as  follows : 

A,  150  shares;  B,  220  shares;  C,  80  shares;  D,  50  shares. 

Par  value  per  share,  f  100. 

What  is  the  capital  stock  of  the  corporation  ? 

2.  How  much  will  a  dividend  of  8  %  yield  each  stockholder  ? 

3.  If  the  annual  profits  are  1 4500,  what  per  cent  dividend  can 
be  declared  ? 


386  CORPORATIONS,  STOCKS,  AND  BONDS 

4.  If  a  5  %  dividend  is  declared  from  the  profits  of  $  4500,  how 
much  will  remain  as  surplus  ? 

5.  If  a  2|  %  assessment  is  levied,  how  much  will  each  stock- 
holder pay  to  the  corporation  ? 

329.  Kinds  of  Stock.  There  are  two  principal  classes  of  stock, 
common  and  preferred. 

Common  Stock  entitles  its  owner  to  a  proportionate  share  of  the 
net  profits  of  the  corporation  when  dividends  are  declared  by  the 
directors.  The  rate  of  dividend  is  not  fixed,  but  depends  upon 
the  success  of  the  business. 

Preferred  Stock  entitles  its  owner  to  a  fixed  per  cent  of  dividend 
provided  the  profits  are  sufficient  to  pay  this  dividend.  Thus,  5  % 
preferred  stock  entitles  the  owner  to  a  5  %  dividend  before  any 
dividends  are  declared  on  the  common  stock. 

Cumulative  Preferred  Stock.  Preferred  stock  may  be  cumulative 
or  non-cumulative.  If  the  stock  is  cumulative,  a  dividend  which 
is  unpaid  one  year  becomes  a  claim  against  the  corporation,  to  be 
paid  out  of  future  profit. 

Participating  Preferred  Stock.  In  some  states  unless  the  pre- 
ferred stock  is  expressly  declared  to  be  non-participating,  the 
preferred  stock  participates  equally  with  the  common  stock  in 
any  dividends  after  both  common  and  preferred  stock  have  re- 
ceived an  equal  dividend. 

That  is,  after  6  %  preferred  stock  has  received  its  6  %  dividend 
and  the  common  stock  has  also  received  6  %,  remaining  dividends 
must  be  shared  equally. 

Example.  The  P^clipse  Carriage  Company  desires  to  build  and 
equip  a  new  factory  at  a  cost  of  #25,000.  A  meeting  of  the  stock- 
holders is  held,  and  it  is  decided  to  issue  5  %  cumulative  non- 
participating  preferred  stock,  in  order  to  obtain  the  required 
funds.  Two  hundred  and  fifty  shares,  with  a  par  value  of  $  100 
dach,  are  issued. 

At  the  end  of  the  year,  a  profit  of  $  9750  is  shown.  How  may 
this  profit  be  divided  among  the  holders  of  the  common  and  pre- 
ferred stock  ? 


CORPORATIONS,  STOCKS,  AND  BONDS  387 

Solution.  5  %  of  ^  25,000  (Preferred  Stock)  =  $  1250,  dividend  on  preferred 
«tock. 

$  9750  —  $  1250  =  $  8500,  remaining  for  dividends  on  common  stock. 
An  8^  %  dividend  may  be  declared  on  the  common  stock. 
If  an  8|  %  dividend  is  declared,  no  surplus  will  remain. 

Written  Work 
if  an  8|  %  dividend  is  declared  on  the  common  stoek : 

1.  How  many  dollars  are  paid  as  dividend  on  each  share  ? 

2.  How  many  dollars  are  paid  as  dividend  on  each  share  of  5  % 
preferred  stock  ? 

The  profits  of  the  second  year  are  only  $500,  and  the  directors 
are  able  to  pay  only  a  2  %  dividend  on  the  preferred  stock.  No 
dividends  are  declared  on  the  common  stock. 

3.  How  much  does  Clark,  who  owns  one  share  of  preferred  stock, 
receive? 

4.  Comstock  owns  five  shares  of  preferred  stock.  How  much 
does  he  receive  ? 

5.  What  is  the  total  unpaid  dividend  on  the  preferred  stock  ? 

The  third  year  a  profit  of  $12,000  is  made.  Settlement  among 
the  shareholders  is  made  as  follows : 

$  12,000     Profits 

750     Last  year's  unpaid  dividends  on  preferred  stock 

$  11,250     Balance 

1,250     Dividends  on  preferred  stock  for  current  year 

$10,000     Available  for  dividends  on  common  stock,  and  surplus 

Clark,  the  owner  of  one  share  of  preferred  stock,  now  receives : 

3  (fo  unpaid  dividends  of  previous  year,     $3.00 

5  %  dividends  of  current  year,  5.00 

$8.00 

Dividends  up  to  10  %  may  be  declared  on  the  common  stock. 

From  this  illustration  you  should  understand: 

a.  The  claim  of  the  owners  of  cumulative  preferred  stock  for  un- 
paid dividends  in  case  sufficient  profits  are  made  in  future  years. 

h.  The  fact  that  preferred  stock  is  usually  an  investment,  but 
common  stock  is  more  of  a  speculation. 


388  CORPORATIONS,  STOCKS,  AND  BONDS 

c.  In  a  business  of  proved  success,  where  the  preferred  stock  is 
non-participating,  the  common  stock  may  be  a  better  investment 
than  the  preferred  stock. 

330.  Buying  Stocks.  Stocks  are  bought  and  sold  at  market 
value  which  may  be  the  same  as  par  value,  but  which  is  usually 
either  more  or  less  than  par.  The  quotation  is  the  statement  of 
market  vali:ffe. 

Example.  Mr.  Ross  purchased  10  shares  of  the  Eclipse  Carriage 
Company's  stock  from  F.  L.  Robbins  at  115.  What  was  the  cost 
of  each  share  ?     What  was  the  total  cost  of  the  stock  purchased  ? 

Solution.     $   115    market  value  per  share 

10     number  of  shares  purchased 
.|1150     cost  of  ten  shares 

When  this  sale  of  stock  is  made,  Robbins  surrenders  his  stock 
certificate  of  fifty  shares  to  the  secretary  of  the  corporation,  who 
issues  a  new  certificate  to  Robbins  for  forty  shares,  and  a  certificate 
to  Ross  for  ten  shares. 

331.  Dealing  in  Stock  through  a  Broker.  Stock  is  usually 
bought  and  sold  through  a  stock  broker.  Brokers  charge  a  certain 
per  cent  of  the  par  value  of  the  stock  which  they  buy  and  sell  for 
customers.  \  of  one  per  cent  of  the  par  value  is  a  common  charge 
for  such  services  when  stock  is  sold  in  large  blocks. 

Examples.  1.  What  is  the  cost  of  100  shares  of  stock  quoted 
at  112J,  purchased  through  a  broker  ?     Brokerage  \  %. 

Solution.    112^^  or  $112.50    market  price  per  share 
i  or  .12|-  brokerage  added  to  cost 

112|or$112.62i  cost  including  brokerage 
100  X  $112,621  =  $11,262.50,  cost  to  purchaser. 

2.  What  is  received  by  the  seller  of  100  shares  of  stock  quoted 
at  11 2|,  sold  through  a  broker  ?     Brokerage  \  %. 

Solution.     112-|^  or  $112.50    price  per  share 

^  or  .12^  brokerage  deducted 

112f  or  $112.37^  returns  per  share  after  deducting  brokerage 
100  X  $112,374-  =  $11,237.50,  returns  from  sale  of  100  shares. 


.     CORPORATIONS,   STOCKS,  AND  BONDS  389 

332.    Profits  from  Stocks.     Stocks  are  usually  purchased  with 
the  hope  of  making  a  profit  in  the  following  ways : 
a.    Holding  tlie  stock  and  receiving  dividends  ;  or 
h.    Selling  the  stock  when  the  market  price  advances. 

Income  from  Dividends.  The  per  cent  of  income  from  dividends 
depends  upon  two  things  : 

a.    The  price  paid  for  the  stock. 

h.  The  dividends,  which  are  always  expressed  in  terms  of  a  per 
cent  of  the  par  value. 

Example.  The  par  value  of  the  common  stock  of  the  Butler 
Dairy  Company  is  $100.00.  A  dividend  of  8%  is  declared. 
What  per  cent  of  income  does  the  holder  of  stock  receive  if  the 
stock  cost  him  119  J,  plus  brokerage  ? 

Solution.    1100.00  par  value  of  stock 
.08   rate  of  dividend 
$  8.00  dividend  per  share 
$119|^  market  value  when  purchased 

\  brokerage 
fl20     cost  per  share 

18.00  (dividend)  -=-  $120  =  6|%  income  on  investment. 

Profit  or  Loss  from  Buying  and  Selling  Stock.  Example.  Perry 
buys  200  shares  of  stock  at  107^,  and  sells  at  108 1,  buying  and 
selling  through  a  broker.     What  profit  does  he  make? 

Solution.    %  107^  market  value  when  purchased 
\  brokerage  added 
f  107^  total  cost  per  share 

^  108f  market  value  when  sold 

\  brokerage  deducted 
$  108|-  received  for  each  share 

^  108|^  received  per  share 
$  107^  cost  per  share 
%  1\  profit  per  share 

$1.25  profit  per  share 
200  number  of  shares 


$250.00   profit  on  200  shares 


390 


CORPORATIONS,   STOCKS,   AND  BONDS 


Written  Work 

1.  What  would  have  been  the  total  loss  if  Perry  had  sold  at 

106|-? 

2.  What  would  have  been  the  total  loss  if  he  had  sold  at  107-^  ? 

3.  7  %  preferred  stock  is  purchased  at  110,  without  brokerage. 
What  per  cent  income  does  the  purchaser  receive  on  his 
investment  ? 

4.  What  is  the  cost  of  7  shares  of  stock,  par  value  100,  pur- 
chased through  a  broker  at  109|?     Brokerage  |  %. 

5.  6 J  %  dividends  are  declared  on  this  stock.  What  per  cent 
income  does  the  purchaser  receive  on  his  investment  ? 

The  following  is  a  partial  list  of  the  quotations  of  a  day's  sales 
by  brokers  on  the  New  York  Stock  Exchange.  Current  quota- 
tions can  be  found  in  the  daily  newspapers. 


Sales 

Description 

Open 

High 

Low 

Close 

1,200 

Am.  Smelting  pfd. 

1041 

105 

102 

103i 

2,300 

Am.  Sugar  common 

108| 

108f 

107 

108J 

400 

Am.  Sugar  pfd. 

113| 

113f 

1121 

11 2i 

1,600 

Central  Leather  pfd. 

96| 

971 

96| 

97i 

2'?,900 

C.  M.  &  St.  P.  common 

105i 

106| 

104 

106i 

400 

C.  M.  &  St.  P.  pfd. 

14H 

141^ 

140 

141 

6.  What  is  received  for  400  shares  of  Am.  Smelting  pfd.  sold 
through  a  broker  at  the  opening  price  in  the  table  ?  Brokerage 
\1o. 

7.  What  is  the  cost  of  400  shares  of  this  stock  if  purchased 
through  a  broker  ?     Brokerage  \  % . 

Note.  Other  problems  may  be  given  by  the  teacher,  either  from  the  above  table 
or  from  the  quotations  of  sales  of  stock  printed  in  the  daily  newspapers. 

Written  Review 

Martin,  Owen,  and  Rathbun  wish  to  organize  a  corporation. 
They  circulate  a  subscription  list,  on  which  they  receive  subscrip- 
tions for  the  entire  authorized  capital  stock,  as  follows : 


CORPORATIONS,   STOCKS,   AND  BONDS 


391 


g)ub0crtption  Mat 
The  Roadbed  Grader  Company 

We,  the  undersigned,  hereby  subscribe  for  the  number  of  shares  and  the  amount 
of  the  Capital  Stock  of  the  Roadbed  Grader  Company,  set  opposite  our  names,  agree- 
ing to  pay  calls  upon  the  said  stock  as  they  shall  be  made  by  the  directors  of  company. 


Number  of  Shares 


^ 


^^/j- 
.^^ 


o^^^^..^^,^.^je^^  ^£^> 


Jc^A-  (fr^M^u^€^ 


Qit£.^L:^xU3^t£i^^.^l^&tt^.^AsA£^ 


/S^OOO       I 


H: 


.  Clcoeyi^ '^ 


O^.^/..^^^,^.  ^^  <^J^^^^ 


J).^.:^jn^AJnj^j 


^^t^>z^v:y    '^C<Ceg^,<^-^ 


rnoo 


6\:€)^^y>AL     ^.^y^^^ 


^^,  Tf^U.^^..^ 


3.00  0 


^.^^^--^=<:^^.2<^ 


1.  What  is  the  capital  stock  of  the  company  ? 

2.  Into  how  many  shares  is  the  capital  stock  divided  ? 

3.  What  is  the  par  value  of  each  share  of  stock  ? 

4.  How  many  votes  does  each  stockholder  have  in  the  meetings 
of  the  stockholders  ? 

5.  Which  two  of  the  stockholdei's  have  votes  enough  (combined) 
to  control  the  management  of  the  corporation  ? 

6.  The  Roadbed  Grader  Company  is  duly  organized,  and  a  call 
is  made  on  each  of  the  subscribers  for  one  half  of  his  subscription, 
payable  on  September  1.  Martin,  Owen,  and  Sanders  pay  the 
call  on  September  1.  How  much  is  received  by  the  treasurer  of 
the  company  on  that  date? 

7.  Rathbun  pays  his  "  call "  on  September  6,  and  is  charged 
6  %  interest  on  the  %  5500  for  the  5  days  during  which  the  call 
remained  unpaid.  How  much  does  Rathbun  pay,  including  call 
and  interest  ? 

8.  Wilbur  pays  his  call  on  September  10,  including  interest 
on  the  delinquent  payment.  Mr.  Wilbur  sends  a  check  to  the 
treasurer  for  % . 


392  CORPORATIONS,  STOCKS,  AND  BONDS 

9.    Call  is  made  for  one  quarter  of  the  subscriptions,  payable 
on  September  20.     The  subscribers  pay  as  follows : 
Martin,  September  20 ; 
Owen,  September  20  ; 
Sanders,  September  22  ; 
Wilbur,  September  25 ; 
Rathbun,  September  27.  - 
How  much  does  each  subscriber  pay,  including  interest? 

10.  Final  call  for  subscriptions  is  made  payable  on  October  1, 
at  which  time  each  of  the  subscribers  pays  the  balance  of  his 
subscription.     How  much  does  each  subscriber  pay  ? 

11.  The  net  profits  the  first  year  were  $4075.  How  much  is 
the  income  tax  ? 

12.  How  much  profit  remains  for  dividends  and  surplus? 

13.  A  6%  dividend  is  declared  on  the  stock.  The  total 
dividend  amounted  to  % . 

14.  What  was  the  amount  of  the  surplus  ? 

15.  What  was  the  amount  of  dividend  received  by  each 
stockholder? 

16.  Considering  {a)  the  dividends,  and  (5)  the  surplus,  if  you 
owned  a  share  of  the  stock  of  the,  Roadbed  Grader  Co.,  would 
you  be  willing  to  sell  it  at  par  ? 

17.  The  net  profits  for  the  second  year  were  $4690.  After 
paying  the  income  tax,  how  much  remains  ? 

18.  What  is  the  largest  per  cent  of  dividend  which  the  direc- 
tors can  declare  out  of  the  second  year's  profits  and  accumulated 
surplus  ? 

19.  What  amount  of  dividend  would  each  stockholder  receive  ? 

20.  After  the  payment  of  the  dividend  indicated  in  question 
18,  how  much  surplus  remains  ? 

21.  Rathbun  sells  7  shares  of  his  stock  to  S.  F.  Cromer  at  114|, 
without  brokerage.     How  much  does  Rathbun  receive  ? 

22.  The  Roadbed  Grader  Company  issues  $15,000.00  of  6  % 
non-participating  stock,  which  it  sells  at  103.  How  much  does 
the  company  receive  for  the  stock  ? 


CORPORATIONS,  STOCKS,  AND  BONDS  393 

23.  The  stock  is  issued  in  $  100  shares  and  is  sold  to  the  fol- 
lowing persons : 

F.  R.  Gridley,  45  shares, 

G.  C.  Moore,  105  shares. 
How  much  does  each  pay  for  his  stock  ? 

24.  The  net  earnings  for  the  third  year  were  $6280.00,  which 
were  distributed  as  follows  : 

2  %  income  tax  on  net  earnings. 

Dividends  on  preferred  stock,  $ . 

The  directors  declare  $  4000.00  dividends  on  the  common  stock. 
What  is  the  per  cent  of  dividend  on  the  common  stock  ? 

25.  What  is  the  amount  of  surplus  remaining  from  this  year's 
profits  ?     What  is  the  total  surplus  accumulated  to  date  ? 

26.  What  per  cent  of  income  do  the  holders  of  the  preferred 
stock,  who  purchased  it  at  103,  without  brokerage,  receive  on  their 
investment  ? 

27.  F.  R.  Taylor  and  J.  E.  Price  engaged  in  partnership. 
Taylor  invested  8  6000.00  and  Price  invested  $9000.00.  The 
business  was  conducted  as  a  partnership  for  several  years,  when 
it  was  decided  to  reorganize  as  a  corporation.  A  statement  of 
resources  and  liabilities  showed  that  the  net  capital  of  the  partner- 
ship was  $28,619.50.  The  corporation  was  organized  with  a 
capital  stock  of  $25,000.00.  The  capitalization  was  how  much 
larger  than  the  actual  net  resources  of  the  firm  ? 

28.  The  stock  was  divided  between  Taylor  and  Price  in  pro- 
portion to  their  original  investment.  If  the  stock  was  issued  in 
$  100  shares,  how  many  shares  did  each  partner  receive  ? 

29.  Burns,  Randall,  and  Anderson  were  partners.  Burns  in- 
vested $  8000,  Randall  $  9000,  and  Anderson  $  18,000.  They  de- 
cided to  organize  as  a  corporation  with  a  capital  stock  of  $  50,000. 
$  45,000  of  the  stock  was  distributed  among  the  partners  in  pro- 
portion to  their  original  investments.  How  many  $  100  shares 
did  each  receive  ? 

30.  The  remaining  stock  is  sold  to  Chapman  at  98|-.  How 
much  did  Chapman  pay  for  his  stock  ? 


394  CORPORATIONS,  STOCKS,  AND  BONDS 

31.  The  profits  for  the  first  year,  after  paying  the  income  tax, 
were  $  4500.     What  dividend  could  be  declared  on  the  stock  ? 

32.  A  corporation  is  organized  with  §100,000  of  common  stock 
and  $  50,000  of  participating  5  %  preferred  stock.  Dividends  of 
$13,500  are  declared.  What  is  the  total  amount  of  dividends 
paid  on  the  common  stock  ?  on  the  preferred  stock  ?  What  rate 
of  dividend  does  the  holder  of  a  share  of  preferred  stock  receive  "^ 
What  rate  of  dividend  does  the  holder  of  a  share  of  common 
stock  receive  ? 

333.  Bonds.  When  an  individual  borrows  money,  he  usually 
gives  a  promissory  note. 

When  a  corporation  borrows  money  in  large  amounts,  it  usually 
issues  bonds. 

Bonds  are  the  promissory  notes  of  a  corporation.  They  are 
usually  issued  in  denominations  of  $1000.00,  although  there  are 
bonds  of  smaller  amounts.  There  is  an  increasing  tendency  to 
issue  bonds  in  denominations  of  $500.00  or  1100.00,  so  that  they 
may  be  sold  to  small  investors. 

Bonds  are  issued  by  : 

Business  Corporations,  called  Industrial  Bonds 

U.  S.  Government  called  Government  Bonds 

State  Governments  called  State  Bonds 

Cities  called  Municipal  Bonds 

Counties  called  Municipal  Bonds 

School  Districts  called  Municipal  Bonds 

Security  of  Bonds.  A  first-mortgage  bond  is  secured  by  a 
mortgage  on  the  property  of  the  corporation.  If  the  bond  is  not 
paid,  the  property  of  the  corporation  may  be  sold  to  pay  the  bond- 
holders. 

Second-mortgage  and  third -mortgage  bonds  are  also  secured  by 
mortgage  on  the  property,  but  the  bondholders  are  paid,  if 
the  mortgages  are  foreclosed,  in  the  numerical  order  of  the 
mortgages. 

Maturity  of  Bonds.  A  bond  states  the  time  at  which  the 
principal  is  payable.     Some  bonds  state  that  the  corporation  re- 


CORPORATIONS,   STOCKS,  AND  BONDS  395 

serves  the  right  to  redeem  the  bond  at  any  time  after  a  specified 
date,  either  at  par  or  at  some  specified  rate  above  par. 

Interest.  Bonds  bear  interest  payable  annually,  semi-annually, 
or  quarterly,  as  specified.  The  method  of  collecting  the  interest 
depends  upon  whether  the  bond  is 

a,  A  Registered  Bond,  or 

h.  A  Coupon  Bond. 

When  a  person  owns  a  registered  bond,  his  name  is  recorded  on 
the  books  of  the  corporation.  When  the  interest  is  due,  a  check 
is  sent  to  the  bondholder  in  payment. 

A  coupon  bond  is  one  to  which  small  coupons  are  attached, 
there  being  one  coupon  for  each  interest  payment.  For  example : 
a  bond  maturing  in  ten  years  with  interest  payable  quarterly 
would  have  forty  coupons.  On  the  date  when  each  interest  pay- 
ment is  due,  the  coupon  bearing  that  date  is  clipped  from  the 
bond  and  delivered  to  a  bank  to  collect,  or  it  may  be  collected 
directly  from  the  treasurer  of  the  corporation. 

Value  of  Bonds.  Bonds,  unlike  common  stock,  pay  a  fixed 
income.  The  market  value  of  a  bond  may  be  above  or  below 
par,  depending  in  general  upon  the  security  and  the  rate  of 
interest. 

Bonds  are  usually  known  by  the  name  of  the  issuing  corporation 
or  government,  the  nature  of  the  security,  the  rate  of  interest,  and 
the  date  of  maturity.  Thus  first-mortgage  bonds  issued  by  the 
Eclipse  Carriage  Company,  bearing  5%  interest  and  payable  in 
1925,  would  be  called  Eclipse  Carriage  Company,  1st  Mortgage 
5  %  Bonds,  1925. 

334.  Buying  and  Selling  Bonds.  When  a  bond  is  sold,  the  buyer 
usually  pays  not  only  the  market  value  of  the  bond,  but  also  the 
interest  which  has  accrued  since  the  last  interest  day. 

Example.  Murdock  owned  an  Eclipse  Carriage  Company  5% 
bond  which  he  wished  to  sell.  The  par  value  of  the  bond  was 
i  1000.00,  and  it  was  quoted  at  95.  Henderson  bought  the  bond 
on  April  1,  at  its  market  value  plus  accrued  interest.  Interest 
is  payable  semi-annually,  June  1  and  December  1.  How  much 
did  Murdock  receive  ? 


396  CORPORATIONS,  STOCKS,  AND  BONDS 

Solution.  Since  the  bond  was  sold  at  95,  the  owner  received  95  %  of  its 
par  value.  95  ^^  ^^  ^  lOOO.OO  =  $  950.00. 

Interest  at  5  %  has  accrued  on  the  bond  from  December  1  to  April  1,  four 
months. 

Interest  on  $  1000  for  4  months  at  5  %  =  $  16.67,  accrued  interest. 
$950.00     market  value  of  bond 

16.67     accrued  interest 
$966.67     selling  price 

Many  banks  and  trust  companies  buy  an  entire  series  of  bonds 
from  corporations  and  sell  them  to  investors.  Prices  are  quoted 
by  these  bond  houses  in  the  following  ways : 

Price,  Par  and  Accrued  Interest ; 

Price,  at  the  Market  and  Accrued  Interest. 

335.  Dealing  in  Bonds  through  a  Broker.  When  bonds  are  pur- 
chased or  sold  through  a  broker,  brokerage  is  charged  in  the  same 
manner  as  when  stocks  are  transferred.  -^  %  of  the  par  value  of 
the  bonds  is  the  customary  brokerage  for  large  transfers. 

Written  Work 

1.  S.  &  J.  6%  coupon  bonds  are  quoted  at  104  and  accrued 
interest.  Interest  payable  June  1  and  December  1.  What  is  the 
cost  of  a  i500  S.  &  J.  bond  purchased  on  August  15  at  the 
market  and  accrued  interest  ?     No  brokerage. 

2.  In  delivering  the  coupon  for  collection  on  December  1,  the 
owner  files  a  certificate  claiming  exemption  under  the  income  tax 
law.     What  is  the  amount  of  interest  which  he  receives  ? 

3.  What  would  the  bond  have  cost  if  purchased  through  a 
broker?     Brokerage  |^%. 

4.  A  bond  house  quotes  Murdock  Apartment  5|  %  bonds  of 
81000.00  at  par  and  accrued  interest.  Interest  due  March  26 
and  September  26.  What  is  the  cost  of  a  bond  purchased  May 
12  ?     October  19  ? 

5.  Laclede  Gas  Light  Company's  $1000  5%  bonds  were 
quoted  by  the  Harris  Trust  and  Savings  Bank  at  101^  and 
interest.  Semi-annual  interest  payable  April  1  and  October  1. 
What  is  the  cost  of  a  bond  purchased  June  15  ? 


CORPORATIONS,  STOCKS,  AND  BONDS 


397 


6.  Wilmington  Power  Company's  5%  bonds  are  quoted  at 
97J  and  interest.  Interest  payable  semi-annually  January  1  and 
July  1.  The  Wilmington  Power  Company  reserves  the  right  to 
redeem  the  bonds  on  January  1,  1919,  or  on  any  interest  day 
thereafter  at  105  and  interest. 

What  is  the  cost  of  a  1 1000  bond  purchased  October  15,  1917, 
at  the  quoted  price  ? 

If  the  bond  is  redeemed  on  July  1,  1920,  what  gain  is  made  by 
the  increase  in  the  redemption  price  over  the  purchase  price  ? 

The  following  is  a  partial  list  of  a  day's  transfers  of  bonds 
through  Chicago  Brokers.     Brokerage  ^%. 


No.  Sold 

Par  Value 

Description 

Open 

High 

Low 

Close 

1 

67 

16 

214 

^1000.00 
1000.00 
1000.00 
1000.00 

Armour  4^'s 
Chicago  City  Ry.  5's 
Com.  Edison  5's 
Peo.  Gas  5's 

92 
lOOf 

lOlf 
99^ 

92 

loii 

lOlf 
99| 

92 

100^ 

lOlf 

99i 

92 

lOOi 

lOlf 

99| 

7.  What  was  the  cost  of  5  Chicago  City  Ry.  11000  bonds, 
purchased  at  the  opening  price  in  the  table  ? 

8.  What  did  the  seller  receive  for  these  bonds?  How  much 
was  the  brokerage  on  the  sale  ? 

9.  What  was  the  gain  or  loss  from  purchasing  60  Peo.  Gas 
$  1000  bonds  at  the  opening  price  and  selling  them  at  the  closing 
price  ?     Brokerage  J  %  on  purchase  and  -|  %  on  sale. 


TABULATIONS   TO   PROMOTE  EFFICIENT 
MANAGEMENT 

CHAPTER   XLII 
BUYING  EXPENSES;  SELLING  EXPENSES;  NET  PROFIT 

336.  Expenses  and  Profits.  In  Chapter  XXIII  the  principles  of 
gross  earnings  were  discussed.  You  have  now  studied  many  of 
the  expenses  incurred  in  conducting  a  business,  and  are  ready  to 
consider  the  problems  which  arise  in  computing  net  profit. 

Net  Profit  is  the  difference  between  the  gross  earnings  of  an 
enterprise  and  the  total  expense  of  conducting  it. 
Expenses  are  divided  into  two  classes : 
Buying  Expenses. 
Selling  Expenses. 

337.  Buying  Expenses  include  all  the  costs  of  buying  goods, 
such  as  freight  and  drayage,  customs  duties  on  goods  imported, 
commissions  of  purchasing  agents,  insurance,  and  the  cost  of 
keeping  goods  in  warehouses  and  placing  them  on  the  shelves  of 
the  salesroom.  Buying  expenses  are  added  to  the  original  pur- 
chase price  of  goods  to  determine  the  total  cost.     Thus : 

Prime  Cost  of  Merchandise  is  the  original  or  purchase  price  ; 
Total  Cost  of  Merchandise  is  the  prime  cost  plus  the  buying 
expenses. 

Example.  A  retail  furniture  store  purchases  goods  during  the 
year,  amounting  to  $36,450.00.  This  is  the  prime  cost.  The 
freight,  drayage,  rent  of  warehouse,  labor  of  warehouse  employees, 
and  other  costs  of  placing  the  goods  in  the  salesroom  are  $2187.00. 

What  is  the  total  cost  of  the  merchandise  purchased? 

Solution.  $36,450.00     Prime  cost 

2,187.00     Buying  expenses 
$38,637.00    Total  cost 

338.  Marking  Cost  of  Goods.  When  the  cost  price  is  marked  on 
goods,  some  merchants  add  a  certain  per  cent  to  the  prime  cost  to 
cover  the  buying  expenses.  The  records  of  previous  years  are 
used  as  a  basis  to  determine  the  per  cent  to  be  added. 

398 


BUYING   EXPENSES  399 

In  the  illustration  on  page  398,  the  prime  cost  is  $36,450.00, 
and  the  buying  expenses  12187.00,  or  6%  of  the  prime  cost. 
The  furniture  dealer  might  say,  "Next  year's  buying  expenses 
will  probably  be  about  the  same  as  they  were  this  year,  and  I  will 
therefore  add  6  %  to  the  prime  cost  to  cover  them." 

A  safer  method,  however,  is  to  base  the  computation  on  the 
average  expenses  of  several  years. 

Yeae  Prime  Cost  Bttting  Expenses 


1916 

835,275.00 

$1840.13 

1917 

41,391.00 

2069.55 

1918 

62,387.00 

3618.45 

1139,053.00  $7528.13 

$7528.13  -  $139,053.00  =  5.41+%. 
For  convenience,  5.4%  probably  would  be  adopted  as  the  per 
cent  of  buying  expenses. 

Illustration.  An  article  cost  $  8.  At  what  price  is  it  marked  to 
cover  buying  expenses  ? 

Solution.  1 8  Prime  cost 

■055  Per  cent  of  buying  expenses 

$    .44  Buying  expenses 

$  8.00  Prime  cost 

.44  Buying  expenses 

$8.44  Total  marked  cost 

Written  Work 

The  prime  cost  of  a  merchant's  purchases  and  the  buying  ex- 
penses for  several  years  are  given  below.  Find  the  per  cent  of  buy- 
ing expenses  for  each  year  and  the  average  for  the  entire  interval. 

Yeab  Purchases  Buying  Expenses 

1.  1914  $  9,426.90  $  643.92 

1915  12,318.26  812.29 

1916  14,126.29  830.12 

1917  11,341.72  690.19 

1918  14,985.29  752.29 

2.  1916  39,286.26  2326.80 

1917  47,562.83  3146.29 

1918  59,286.28  4210.08 


400 


BUYING  EXPENSES 


3.  The  prime  cost  of  merchandise  in  a  certain  store  is  increased 
8%  to  include  buying  expenses;  the  selling  price  is  determined 
by  adding  9%  to  the  total  cost.  Mark  the  total  cost  (using 
"blacksmith"  as  the  key  and  "g"  as  a  repeater)  and  the  selling 
price  (in   figures),  of   articles,   the  prime  cost  of  which  was  as 

follows  :  Stock  No.  Prime  Cost 

A  326  $2.19 

A  394  6.25 

F  246  '  .90 

A  385  2.78 

4.  The  manager  of  one  of  the  departments  in  a  large  store 
adds  6  %  to  the  prime  cost  to  cover  the  buying  expenses.  He  re- 
ceives quotations  of  prices  from  manufacturers  who  offer  different 
discounts.  He  prepares  a  table  showing  the  total  cost  after  de- 
ducting the  discount  offered  and  adding  the  6  %  buying  expenses. 
The  following  is  a  similar  table  which  you  will  complete : 


.00 

.25 

.50 

.75 

1 

Less  2% 
Plus  6% 

Less  5% 
Plus  6% 

+  C% 

-2% 

+  c% 

-5% 

+  6% 

-2% 

-5% 
+  6% 

+  6% 

-2% 
+  0% 

-5% 
+  6% 

-7% 

+  6% 

0 

1 

2 
3 
4 
5 
6 
7 
8 
9 
10 

1.0388 

1.007 

.9858 

.2597 

.25175 

.24645 

5.  By  referring  to  the  table,  find  the  total  cost,  including  buy- 
ing expenses,  of  an  article  quoted  at  12.25  less  5% ;  $3  less  2%. 

Refer  to  the  table,  and  find 

6.  Which  is  the  better  price,  and  how  much  better:  81.75 
each,  less  2  %,  or  $2  each,  less  7  %  ?  How  much  will  be  saved  by 
purchasing  one  gross  at  the  cheaper  quotation  ? 


SELLING  EXPENSES 


401 


339.  Selling  Expenses.  After  the  goods  have  been  placed  on 
sale,  all  further  costs,  such  as  rent  of  store,  salaries  of  clerks,  ad- 
vertising, heat  and  light,  delivery,  store  supplies,  insurance  and 
taxes,  depreciation  and  shrinkage,  bad  debts,  and  general  ex- 
penses, are  considered  as  selling  expenses. 

• 

340.  Finding  the  per  cent  of  selling  expenses.  The  per  cent  of 
selling  expenses  is  a  matter  of  valuable  information  to  a  mer- 
chant.    It  is  determined  by  the  formula : 

Selling  Expenses  -h  Gross  Sales  =  %  of  Selling  Expenses. 

Example.  A  merchant's  gross  sales  during  one  year  are 
f  124,265  ;  the  selling  expenses  for  the  same  year  are  $29,078.01. 
The  selling  expenses  are  what  per  cent  of  the  gross  sales  ? 

Solution.    $  29,078.01  h-  $  124,26.5.00  =  23.4  ^o. 

341.  Increase  of  Selling  Expenses.  During  recent  years,  as 
shown  by  the  graph  reprinted  from  System^  a  Magazine  of  Business^ 
selling  expenses,  such  as  advertising,  delivery,  etc.,  have  greatly 
increased. 


27 
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Department  Store  (Annual  Sales  $17,000,000  in  1912) 
Dry  Goods  Store  (      ,.         „         $150,000 ..    ..   ) 
Small  Store            (      m         ..           $25,000"    ••  ) 

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90                             1895                            1900                             1905                            1910               19U  | 

402 


SELLING  EXPENSES 


Oral  Work 

Trace  the  rise  in  the  per  cent  of  selling  expenses  in  each  busi- 
ness, stating  what  per  cent  the  selling  expenses  in  each  business 
are  of  the  gross  sales  in  each  year. 

Written  Work 

The  following  statistics  are  reprinted  from  System^  and  show 
the  result  of  an  investigation  made  by  that  magazine  to  determine 
average  or  standard  per  cents  of  selling  expenses  in  various  busi- 
nesses. 

Find  what  per  cent  each  item  of  expense  is  of  the  total  sales. 

Find  what  per  cent  the  total  selling  expenses  are  of  the  sales. 


Dky  Goods  Stoke       General  Store 


Gross  Sales, 
$  50,000.00 


Gross  Sales, 
$  50,000.00 


Shoe  Stokb 


Gross  Sales, 
$  25,000.00 


Rent 

Salaries 

Advertising 

Heat  and  light 

Delivery 

Supplies 

Insurance  and  taxes  .  .  . 
General  expense  .... 
Depreciation  and  shrinkage 
Bad  debts 


$1,550.00 

4,800.00 

750.00 

200.00 

450.00 

200.00 

.  550.00 

2,200.00 

700.00 

150.00 


.$1,154.85 
4,067.09 
351.48 
251.04 
954.01 
150.63 
200.84 
150.63 
301.27 
150.63 


I    778.13 

2,786.21 

376.51 

225.91 

75.30 

100.40 

301.21 

1,029.14 

150.61 

25.10 


Vehicle  Store 


Gross  Sales, 
$57,000.00 


Hardware  Store     Furniture  Stork 


Gross  Sales, 
$  46,000.00 


Gross  Sales, 
$  100,000.00 


Rent 

Salaries 

Advertising 

Heat  and  light ;     .     .     .     . 

Delivery 

Supplies 

Insurance  and  taxes  .  .  . 
General  expense  .... 
Depreciation  and  shrinkage 
Bad  debts 


$1,094.63 
5,818.81 
633.73 
345.67 
518.51 
230.45 
460.90 
230.45 
403.28 
115.22 


$  1,305.61 
5,042.35 
405.20 
226.10 
270.13 
180.08 
495.23 
360.17 
225.10 
180.08 


3,507.36 
8,317.60 
2,906.15 

801.70 
1,102.33 

501.06 
1,402.97 
1,803.82 
1,904.03 
1,202.54 


SELLING  EXPENSES 


403 


Rent 

Salaries 

Advertising 

Heat  and  light 

Delivery 

Supplies  .     , 

Insurance  and  taxes .  .  . 
General  expense  .... 
Depreciation  and  shrinkage 
Bad  debts 


Clothing  Stoke 


Gross  Sales, 
$  60,000.00 


1,322.24 

5,469.29 

2,043.47 

180.31 

360.61 

120.20 

661.12 

1,681.84 

721.22 

240.41 


Dbxjo  Stoke 


Gross  Sales, 
$  20,000.00 


I    924.66 

2,191.01 

522.64 

160.81 

80.40 

60.30 

281.40 

482.42 

100.50 

40.20 


Jewelry  Store 


Gross  Sales, 
$  80,000.00 


$  1,080.40 

3,361.23 

1,050.38 

180.07 

30.01 

270.10 

540.20 

630.23 

360.13 

90.03 


Save  your  results  for  use  in  the  problems  which  follow. 

342.    Efficient  Management  to  Determine  Economies  and  "Leaks." 

When  a  merchant  has  a  reliable  standard  with  which  to  com- 
pare the  various  per  cents  of  selling  expenses  in  his  business,  he 
is  able  to  determine  the  items  of  expense  which  are  too  large. 


Written  Work 

A  dry  goods  store  has  gross  sales  during  one  year  amounting 
to  i  40,000.00.     The  expenses  are  as  follows  : 

165.00 
180.00 
155.00 
120.00 
42.00 


Rent  $1200.00 

Salaries  3240.00 

Advertising  250.00 

Heat  and  light        225.00 
Delivery  1135.00 


Supplies 

Insurance  and  taxes 
General  expense 
Depreciation  and  shrinkage 
Bad  debts 


1.  Each  item  of  expense  is  what  per  cent  of  the  gross  sales  ? 

2.  Th9  total  selling  expenses  are  what  per  cent  of  the  sales  ? 

3.  Accepting  the  per  cents  found  in  the  dry  goods  store  prob- 
lem on  page  402  as  a  standard,  determine  which  expenses  are 
larger  than  the  standard,  and  which  are  smaller. 

4.  Complete  the  following  table  : 


404 


NET  PROFIT 


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NET  PROFIT  405 

5.  Plot  a  curve  in  black  ink  to  show  the  per  cent  of  gross  earn- 
ings in  each  department.  Plot  a  curve  on  the  same  paper  in  red 
ink  to  show  the  per  cent  of  net  profit  or  net  loss  in  each 
department. 

Suggestion.  Draw  a  line  horizontally  across  the  paper  representing  0  %; 
scale  the  paper  to  show  per  cents  of  gain  above  this  line,  and  per  cents  of  loss 
below  the  line. 

343.  Common  Omissions  in  Computing  Selling  Expenses.  Mer- 
chants sometimes  underestimate  their  selling  expenses  by  omitting 
the  following  : 

(a)  Rent  on  store  owned  by  the  proprietor. 

A  man  who  owns  his  own  store  should  include  among  his  ex- 
penses the  sum  which  he  would  be  able  to  obtain  if  he  rented  the 
store  to  some  other  person,  because  he  loses  this  rent  by  occupy- 
ing the  store  himself. 

(b)  Salaries  of  the  proprietor  and  members  of  his  family  em- 
ployed in  the  store. 

Such  salaries,  even  though  they  may  not  be  paid,  should  be 
included  in  the  expenses,  since  the  proprietor  and  the  mem- 
bers of  his  family  would  probably  be  able  to  obtain  the  salaries 
elsewhere. 

(<?)  Depreciation. 

Store  buildings  and  fixtures  depreciate  in  value,  and  while  such 
depreciation  may  not  be  noticeable,  it  should  be  computed 
annually.  Goods  also  become  shopworn  or  out  of  style  and  the 
depreciation  in  value  should  be  charged  off  in  the  year  in  which  it 
occurs. 

(d)  Bad  debts. 

Careful  merchants  make  every  effort  to  collect  their  accounts, 
but  unless  a  strictly  cash  business  is  conducted,  some  accounts 
are  almost  certain  to  prove  uncollectable.  In  estimating  the 
probable  loss  from  bad  debts,  some  merchants  compute  a  certain 
per  cent  of  the  sales,  while  others  compute  a  certain  per  cent  of 
past  due  accounts. 


406  NET  PROFIT 

Written  Work 

A  merchant  invests  f  5000.00  in  a  general  store.  His  gross 
sales  during  a  certain  year  are  f  17,350.00.  He  owns  his  store 
building  valued  at  i  3000.00.  He  lists  his  selling  expenses  as 
follows  :  Salaries  (one  clerk)     |  600.00 

Advertising  85.00 

Heat  and  light  125.00 

Delivery  140.00 

Insurance  and  taxes         95.00 

General  expenses  110.00 

1.  What  are  the  total  expenses  as  shown  by  the  list  ? 

2.  These  expenses  are  what  per  cent  of  the  gross  sales  ? 
The  following  items  have  been  omitted : 

The  store  building  could  be  rented  for  $  360  per  year. 

The  owner  and  one  member  of  his  family  work  in  the  store.  If 
employed  elsewhere,  the  two  could  earn  $  950. 

7  %  would  be  a  fair  rate  for  depreciation  on  the  building. 

Shop  wear  and  change  of  style  have  decreased  the  value  of 
goods  in  stock,  $  100. 

An  examination  of  this  merchant's  books  shows  that  his  annual 
loss  from  bad  debts  is  about  1  %  of  his  gross  sales. 

3.  Make  a  list  of  the  selling  expenses  of  this  business,  including 
those  which  the  merchant  omitted. 

4.  What  are  the  total  expenses  ? 

5.  The  total  expenses  are  what  per  cent  of  the  gross  sales  ? 

6.  The  cost  of  the  goods  sold  is  1 14,520.00. 
What  is  the  gross  profit  ? 

7.  What  does  the  merchant  consider  to  be  his  net  profit  after 
deducting  the  expenses  as  stated  in  his  list  ? 

8.  After  deducting  his  real  expenses  as  shown  by  your  cor- 
rected list,  did  he  have  a  net  gain  or  a  net  loss?     How  much? 

9.  Find  what  per  cent  each  item  of  selling  expenses  is  of  the 
gross  sales. 


NET  PROFIT  407 

10.  By  comparing  these  per  cents  with  the  average  or  stand- 
ard per  cents,  we  may  find  the  "leaks"  of  this  business. 

Which  of  these  per  cents  are  smaller  than  the  standard? 
Which  of  the  per  cents  are  larger  than  the  standard? 
Although  the  general  expenses  are  large,  they  include  supplies 
for  which  no  separate  charges  are  made. 

11.  What  is  the  worst  "leak  "  in  this  business? 

344.  Reducing  the  Per  Cent  of  Selling  Expenses  by  Increasing 
the  Gross  Sales.  It  is  evident  that  as  the  per  cent  of  selling  ex- 
penses increases,  other  factors  remaining  the  same,  the  per  cent 
of  profit  on  the  sales  decreases.  It  is  therefore  desirable  to  de- 
crease the  per  cent  of  selling  expenses.  The  per  cent  of  selling 
expenses  may  be  reduced  by 

Reducing  the  selling  expenses, 

or 

Increasing  the  gross  sales. 

Written  Work 

1.  If  the  gross  sales  were  $50,000.00  and  the  selling  expenses 
$10,000.00,  what  was  the  per  cent  of  selling  expenses? 

2.  If  the  selling  expenses  could  be  reduced  to  $8000.00,  with- 
out reducing  the  gross  sales,  what  would  be  the  per  cent  of  sell- 
ing expenses? 

3.  If  the  selling  expenses  remained  $10,000.00,  and  the  gross 
sales  were  increased  to  $60,000.00,  what  would  be  the  per  cent 
of  selling  expenses? 

4.  If  an  increase  of  the  gross  sales  to  $80,000.00  resulted  in  an 
increase  of  selling  expenses  to  $12,000.00,  what  would  be  the  per 
cent  of  selling  expenses? 

Increasing  the  Gross  Sales.  The  gross  sales  may  be  increased 
in  three  ways  : 

By  increasing  the  selling  price  ;  the  turnover  remaining  the 
same. 

By  increasing  the  turnover  ;  the  selling  price  remaining  the 
same. 


408  NET  PROFIT 

By  increasing  the  selling  price  and  the  turnover. 

Increasing  the  selling  price  of  a  commodity  may  result,  however, 
in  decreasing  the  gross  sales  by  causing  a  decreased  demand. 
For  this  reason  the  more  popular  method  of  increasing  gross 
sales  is  to  sell  at  a  small  profit  and  to  make  frequent  "turn- 
overs." 

The  "  turnover  "  means  the  number  of  times  by  which  the  gross 
sales  exceed  the  average  inventory. 

Thus,  if  the  average  value  of  the  stock  kept  is  i  5000. 00  (selling 
price)  and  the  gross  sales  for  a  year  are  15000.00,  there  is  one 
turnover.  If  the  gross  sales  are  115,000.00,  there  are  three 
turnovers. 

345.  Small  Profits  and  Frequent  Turnovers.  The  following  il- 
lustration shows  how  a  larger  profit  may  be  made  from  several 
turnovers  at  a  small  markup,*  than  by  a  single  turnover  at  a  large 
markup. 

Let  us  suppose  that  a  merchant's  stock  inventories  at  cost 
prices  #10,000.00  (which  includes  buying  expenses).  If  the  sell- 
ing expenses  are  $5000.00,  the  merchant  must  obtain  $15,000.00 
before  he  begins  to  make  any  profit.  This  means  a  markup  of 
50%.  In  order  to  make  a  5%  profit  on  the  cost,  he  must  mark 
his  goods  at  bb  ^o  above  cost.  An  article  costing  fl.OO  must  sell 
for  $1.55.  Thus  a  single  turnover  at  bb^o  markup  will  net  a 
profit  of  1500.00. 

Now  let  us  suppose  that  a  30  %  markup  (selling  an  article  cost- 
ing $1.00  for  $1.30)  will  result  in  two  turnovers  without  increas- 
ing the  selling  expenses. 

Each  turnover  of  a  stock  costing  $10,000  means  gross  sales  of 
113,000.00  ;  two  turnovers  make  the  gross  sales  $26,000.00,  and 
the  gross  profits  $6000.  After  deducting  the  selling  expenses  of 
$5000  a  profit  of  $1000  remains. 

If  a  markup  of  20  %  results  in  four  turnovers  of  stock  cost- 
ing $10,000  with  selling  expenses  of  $6000,  what  is  the  net 
profit  ? 

*  By  "markup"  is  meant  the  per  cent  added  to  prime  cost  and  buying  expenses 
to  cover  selling  expenses  and  profit. 


NET  PROFIT  409 

Written  Work 
1.    A  certain  merchant  takes  an  inventory  once  a  month.     The 
following  are  the  inventories  for  the  year  at  cost  prices. 


January 

127,365.80 

July 

128,346.70 

February 

25,398.25 

August 

28,134.62 

March 

26,285.00 

September 

26,347.80 

April 

26,947.30 

October 

27,228.35 

May 

27,235.80 

November 

30,562.95 

June 

29,165.20 

December 

31,728.73 

What  is  the  average  stock  carried  ? 

2.  Plot  a  curve  on  graphically  ruled  paper  to  show  the 
monthly  inventories. 

3.  The  selling  expenses  for  the  year  are  $  15,342.55,  or % 

of  the  average  inventory. 

4.  If  one  turnover  is  made,  what  must  be  the  per  cent  of 
markup  in  order  to  make  a  net  profit  of  4  % .  on  the  average  in- 
ventory ? 

The   gross  sales  would  be   $ ,  and   the   profit   would   be 

I . 

5.  If  four  turnovers  are  made,  what  is  the  cost  of  the  goods 
sold? 

The  selling  expenses  increased  to  $18,420;  what  may  be  the 
cause  of  the  increase  in  the  selling  expenses  ? 

6.  The  selling  expenses  in  Problem  5  are  what  per  cent  of 
the  cost  of  the  goods  sold  ? 

7.  In  order  to  make  a  total  profit  of  4  %  of  the  average  in- 
ventory during  the  year,  what  per  cent  of  profit  must  be  made  on 
each  turnover  ? 

8.  What  is  the  necessary  per  cent  of  markup  on  each  turn- 
over, selling  expenses  being  16.5  %  ? 

9.  What  would  be  the  selling  price  of  an  article  which  cost 

12? 


410  NET   PROFIT 

What  is  the  profit  or  loss  in  each  of  the  following  ? 

Average  Inventory  Selling  Expenses  Turnovers  Markup 

10.  $  2,000.00  I     432.00  1  20% 

11.  8,340.25  1,365.00  3  15% 

12.  12,375.70  3,174.25  4J  13% 

13.  27,320.00  12,278.60  9  8% 

14.  With  $  12,000  invested  in  stock,  and  with  selling  expenses 
of  $  4000,  how  much  profit  is  made  by 

3  turnovers  with  a  markup  of  12  %  ? 
5  turnovers  with  a  markup  of  10  %  ? 
8  turnovers  with  a  markup  of  6  %  ? 


CHAPTER   XLTII 
FINDING  THE  PROFITABLE  DEPARTMENTS 

In  a  business  which  is  divided  into  several  departments,  one  or 
more  departments  may  be  operating  at  a  loss,  while  the  business 
as  a  whole  shows  a  profit.  Unless  these  departments  where  losses 
occur  are  discovered  and  expenses  curtailed,  or  gross  sales  or  gross 
profits  increased,  such  departments  remain  a  burden  to  the  business. 
In  order  to  find  the  profit  by  departments,  the  following  facts 
must  be  known  for  each  department ; 

Cost  of  Goods  Sold ; 

Gross  Sales ; 

Expenses. 
The  first  two  of  these  facts  may  be  easily  determined,  since 
each  department  may  be  considered  as  a  separate  store,  with  sepa- 
rate records  of  purchases,  sales,  and  inventories.  But  the  diffi- 
culty comes  in  determining  the  expenses  —  a  difficulty  due  to  the 
fact  that  the  expenses  are  of  two  kinds. 

346.  Local  and  Overhead  Expenses.  Local  Department  Ex- 
penses consist  of  items  of  expense  paid  for  each  department 
separately,  such  as  salaries  of  clerks  who  work  in  only  one  depart- 
ment. There  is  no  difficulty  in  determining  the  local  expenses 
of  each  department. 

Overhead  Expenses  consist  of  all  items  of  expense  paid  by  the 
store  as  a  whole  for  the  general  benefit  of  all  departments. 
Among  these  expenses  are  Rent,  Taxes  and  Insurance,  Heat  and 
Light,  Janitor  and  Elevator  Service,  Salaries  of  Executive  and 
Office  Employees,  Delivery  Service,  Advertising. 

347.  Prorating  Overhead  Expenses.  All  overhead  expenses 
must  be  divided  among  the  various  departments  according  to 
some  reasonable  basis.  The  proper  basis  of  division  depends  on 
the  nature  of  the  expense.  The  method  of  distribution  is  called 
prorating. 

411 


412  FINDING  THE  PROFITABLE  DEPARTMENTS 

Bases  of  Prorating  Overhead  Expenses.  The  following  illustra- 
tions show  some  of  the  bases  of  distributing  overhead  expenses. 

a.    Rent :  Prorated  by  floor  space. 

Suppose  a  store  with  four  departments  occupies  a  building  with 
4800  square  feet  of  floor  space.  If  each  department  occupies  1200 
square  feet,  each  should  pay  \  of  the  rent.  But  if  one  department 
occupies  only  400  square  feet,  it  should  be  charged  with  only  ^g 
or  Y^2  of  ^^  rent.  Each  department  should  be  charged  rent  in 
proportion  to  the  floor  space  which  it  occupies.  In  some  con- 
cerns the  relative  values  of  different  floors  and  locations  is  taken 
into  consideration. 

h.  Insurance  and  Taxes  on  Stock :  Prorated  according  to  the 
average  value  of  the  stock  carried  in  each  department. 

c.  Insurance  and  Taxes  on  Building :  Prorated  by  floor  space. 

d.  Heat  and  Light :  Determined  by  separate  meters  or  pro- 
rated by  floor  space. 

e.  Expenses  of  Alterations  Department :  Charged  according  to 
the  actual  expense  of  alterations  made  for  each  department. 

/.  Expenses  of  Returned  Goods  Department :  Prorated  among 
the  various  departments  on  the  basis  of  the  number  of  articles 
returned  to  each  department  by  customers. 

g.  Salaries  and  Expenses  of  Traveling  Salesmen :  Prorated 
according  to  the  sales  made  by  traveling  salesmen  for  each  de- 
partment. 

h.  Advertising :  Prorated  according  to  the  space  occupied  in 
the  advertising  mediums. 

Oral  Work 

Discuss  the  reasons  for  the  basis  of  prorating  adopted  in  each 
instance  above. 

What  would  be  a  reasonable  basis  for  prorating  the  following 
expenses? 

Executive  Salaries; 
Salaries  of  Office  Force ; 
Cost  of  Delivery  Service  ; 
Depreciation  on  Building. 


FINDING  THE   PROFITABLE  DEPARTMENTS  413 

Method  of  Prorating. 

a.    Determine  the  most  reasonable  basis  ; 

h.  Divide  the  total  expenses  by  the  total  number  of  units  of 
the  basis  used,  to  determine  the  prorate ; 

c.  Multiply  the  prorate  by  the  number  of  units  of  the  basis  in 
each  department. 

Example.  The  rent  of  a  store  building  is  1 925,  to  be  prorated 
on  the  basis  of  floor  space.  The  space  occupied  by  each  depart- 
ment is  as  follows: 

Dept.         Dimensions  Area 

I.     15'  X  20'  300  sq.  ft. 

II.     80'  X  40'  3200  sq.  ft. 

III.     25'  X  52'  1300  sq.  ft. 

Total  4800  sq.  ft. 

What  share  of  the  rent  should  be  charged  to  each  department  ? 
Solution.     $  925.00  ^  4800  =  %  .19270,  the  prorate,  or  the  rent  per  square 

foot. 

Dept.  I.     $.19270   prorate 

300   sq.  ft.,  Dept.  I 
$57.81    share  of  rent 

Dept.  II.     $  .19270  prorate 

3200   sq.  ft.,  Dept.  II 
$616.64   share  of  rent 

Dept.  III.     $.19270  prorate 

1300   sq.  ft.,  Dept.  Ill 
$250.51   share  of  rent 

To  check  the  above  computations  : 

$57.81   rent,  Dept.  I 
616.64   rent,  Dept.  II 
250.51   rent,  Dept  III 
$924.96   total  rent 

The  total  rent  thus  computed  is  four  cents  less  than  the  actual 
rent.  A  discrepancy  so  small  is  entirely  justifiable  in  such  com- 
putations. In  order  to  avoid  a  larger  error,  the  prorate  should 
include  as  many  significant  figures  as  there  are  dollars  and  cents 
in  the  expenses.  A  prorate  of  .0932  has  three  significant  figures. 
If  the  expenses  were  136.45,  the  prorate  should  have  four  signifi- 


414 


FINDING  THE  PROFITABLE   DEPARTMENTS 


cant  figures  ;  if  the  expenses  were  13125,  the  prorate  should  have 
six  significant  figures. 

Written  Work 

A  blank  form  similar  to  the  following  illustration  should  be 
prepared  for  each  of  the  following  problems  of  prorating  overhead 
expenses. 

1.    Prorating  rent  by  floor  space : 

Dept.  Floor  Space  Dept.  Floor  Spaob 

260  sq.  ft.  6.  470  sq.  ft. 

380  sq.  ft.  7.  630  sq.  ft. 

694  sq.  ft.  8.  763  sq.  ft. 

876  sq.  ft.  9.  856  sq.  ft. 

340  sq.  ft.  10.  940  sq.  ft. 


1. 
2. 
3. 
4. 
5. 


Total  annual  rent,  136,000. 


Prorating  Rent  by  Floor  Space 

Total  Rent. 
Prorate-- 


Department 

Floor  Space 

Prorated  Eent 

Totals 

2.    Prorating  insurance  on  stock  according  to  the  average  value 
of  the  stock  carried  in  each  department : 

Dept.        Average  Stock                                               Dept.  Average  Stock 

1.  $3,600.00                                   6.  16,890.00 

2.  5,400.00                                  7.  3,750.00 

3.  4,990.00                                  8.  8,460.00 

4.  6,030.00.                                  9.  6,560.00 

5.  3,740.00                                10.  4,700.00 
Cost  of  insurance  on  stock,  $540.00. 


FINDING  THE  PROFITABLE  DEPARTMENTS  415 

3.  Prorating  general  expenses,  heat,  light,  janitor  service,  etc., 
according  to  floor  space. 

The  total  general  expenses  for  the  year  are  f  6346.80.  The 
floor  space  of  the  different  departments  is  given  in  Problem  1. 

4.  Prorating  executive  salaries  and  interest  on  investment, 
according  to  capital  invested  in  each  department,  as  shown  by  the 
average  stock  carried.  The  total  executive  salaries  and  interest 
on  the  investment  for  the  year  are  $12,350,00.  The  average 
stock  carried  in  each  department  is  shown  in  Problem  2. 

5.  Prorating  expenses  of  returned  goods  department  according 
to  the  number  of  sales  returned. 

Dei't.  No.  of  Sales  Ket'd  Dept.    No.  of  Sales  Ket'd 


1. 

1980 

5. 

1746 

2. 

3764 

6. 

1329 

3. 

Goods  purchased  from 

7. 

1426 

this  department  can- 

8. 

1276 

not  be  returned. 

9. 

1362 

4. 

189 

10. 

1147 

The  total  expenses  of  the  returned  goods  department  for  the 
year  are  $375.94. 

348.  Comparing  Profits  or  Losses  by  Departments.  After  the 
overhead  expenses  have  been  prorated  among  the  various  depart- 
ments, and  after  the  sales,  purchases,  local  expenses,  and  other  facts 
of  each  department  have  been  determined,  the  profit  or  loss  and  the 
per  cent  of  profit  or  loss  can  be  computed,  and  the  departments 
compared  on  a  tabulated  form  similar  to  the  one  used  in  the 
written  exercise  on  page  404. 


CHAPTER   XLIV 
FINDING  THE  PROFIT  OR  LOSS  ON  EACH  SALE 

349.  Factors  which  Determine  Cost  of  Each  Sale.  Large  busi- 
ness houses  keep  records  to  show  not  only  the  profit  or  loss  of 
the  entire  store  and  of  each  department,  but  also  the  profit  or  loss 
on  every  sale.  In  order  to  do  this,  a  cost  book  is  prepared,  show- 
ing the  cost  of  every  article  for  sale  in  the  store.  The  cost  shown 
in  the  cost  book  is  the  total  cost ;  it  includes 

a.  the  wholesale  cost  of  the  article ; 
h,  a  share  of  the  buying  expenses  ; 
c.  a  share  of  the  selling  expenses. 

Preparing  the  Cost  Book.  The  three  items  of  cost  required  in 
preparing  a  cost  book  are  found  as  follows  : 

a.  The  wholesale  cost  of  each  article  is  taken  from  the  invoice 
when  the  goods  are  purchased. 

h.  The  share  of  buying  expenses  to  be  added  is  determined  by 
the  following  formulas : 

*  Direct  Buying  Expenses  +  Prorated  Overhead  Buying  Ex- 
penses =  Total  Buying  Expenses. 

Total  Buying  Expenses  ^  Total  Cost  of  Goods  Purchased  =  % 
of  Buying  Expenses  to  be  added  to  the  wholesale  cost  of  each 
article. 

Example.  What  is  the  per  cent  of  buying  expenses  in  a  depart- 
ment reporting  the  following : 

Salaries  of  buyers,  freight,  and  other  direct  buying  expenses, 
$3500. 

Prorated  share  of  overhead  buying  expenses  (warehouse  rent, 
labor,  etc.),  $2400. 

Cost  of  purchases  for  the  year,  184,285.50. 

*  Direct  buying  expenses  are  the  expenses  which  may  be  charged  directly  to  the 
department  purchasing  the  goods. 

416 


FINDING  THE  PROFIT  OR  LOSS  ON  EACH  SALE      417 

Solution.     •!  3500.00     Direct  buying  expenses 

2400.00     Share  of  overhead  buying  expenses 
$5900.00     Total  buying  expenses 
$  5900  -4- 1 84,285.50  =  7%  . 

7  %  is  therefore  added  to  the  cost  of  each  article  to  cover  the  buying  ex- 
penses. 

c.  The  share  of  selling  expenses  to  be  added,  is  computed  by  the 
following  formulas : 

Direct  Selling  Expenses  +  Prorated  Share  of  Overhead  Selling 
Expenses  =  Total  Selling  Expenses. 

Total  Selling  Expenses  -^  Cost  of  Goods  Sold  =  %  of  Selling 
Expenses  included  in  Cost. 

Example.  The  department  furnishing  the  facts  for  the  preced- 
ing illustration  reported  the  following  : 

Salaries  of  salesmen,  and  other  direct  selling  expenses,  85360; 

Prorated  share  of  overhead  selling  expenses,  $7340; 

Cost  of  goods  sold,  $96,153.85. 

What  per  cent  should  be  added  to  the  cost  of  goods  to  cover 
the  selling  expenses? 

Solution.    %  5160.00     Direct  selling  expenses 

7340.00     Overhead  selling  expenses 
$  12,500.00     Total  selling  expenses 
^  12,500  ^  %  96,153.85  =  13  %. 

13  %  would,  therefore,  be  added  to  the  cost  of  each  article  in  this  depart- 
ment to  cover  the  selling  expenses. 

350.  Combining  the  Buying  and  Selling  Expenses.  After  the 
per  cent  of  buying  expenses  and  the  per  cent  of  selling  expenses 
have  been  determined,  the  two  per  cents  are  added,  and  the  re- 
sulting per  cent  of  the  cost  is  added  to  the  cost  of  each  article 
to  cover  all  expenses.  Although  the  per  cents  are  merely  esti- 
mates, determined  from  the  business  of  former  years,  firms  of 
long  experience  use  per  cents  which  the  business  of  the  past 
shows  to  be  approximately  correct. 

Written  Work 
Complete  the  following  table  showing  the  per  cent  of  buying 
expenses,  the  per  cent  of  selling  expenses,  and  the  total  per  cent 
to  be  added  to  the  cost  of  each  article  purchased. 


418      FINDING  THE  PROFIT  OR  LOSS  ON  EACH  SALE 


Dept. 

DiEEOT 

Buying 

Share  of 

Overhead 

Buying 

Total 
Buying 

Purchases, 

Per  Cent 
op 

Inventory, 

PUBOHASES. 

Expenses 

Expenses 

Expenses 

lyiT 

Buying 
Expenses 

Jan.  1,  1917 

191T 

Dollars 

Dollars 

Dollars 

Dollars 

Dollars 

Dollars 

I 

3,500 

00 

2,400 

00 

5,900 

00 

84,285 

50 

7% 

27,624 

85 

84,285 

50 

II 

2,112 

19 

1,354 

25 

69,328 

72 

16,582 

88 

III 

1,565 

58 

1,327 

42 

48,216 

73 

4,532 

42 

IV 

3,402 

51 

3,928 

36 

91,635 

82 

12,013 

16 

V 

926 

39 

712 

46 

23,412 

17 

5,969 

48 

VI 

1,426 

12 

951 

33 

39,624 

17 

2,023 

72 

Total  Cost 

op  Mdsb., 

1917 

Inventory, 

Deo.  31, 

1917 

Cost  of 

Goods  Sold, 

1917 

Direct 
Selling 
Expenses 

Share  of 

Overhead 

Selling 

Expenses 

Total 
Selling 
Expenses 

Per  Cent 
of  Total 
Expenses 

Total 
Pee 

Cent 

Dollars 

Dollars 

Dollars 

Dollars 

Dollars 

Dollars 

111,910 

35 

15,756 

14,217 

9,532 

14,216 

4,162 

4,328 

50 
23 
80 
23 
39 
63 

96,153 

85 

5,160 

6,236 
3,829 
10,560 
1,332 
3,929 

00 
48 
16 
26 
21 
23 

7,340 
5,951 
2,653 
7,326 
1,946 
2,788 

00 
56 
29 
29 
29 
24 

12,500 

00 

13% 

20% 

Save  your  results  for  future  use. 

351.    The  Cost  Book.     The  cost  book  is  ruled  as  in  the  illustra- 
tion below  : 


Article 

No. 

Dept.  I 

Dept.  II 

Dept.  Ill 

Dept.  IV 

Dept.  V 

Dbpt.  VI 

1 
2 
3 
4 
5 

14 

68 

6 
7 
8 
9 
10 

11 
12 
13 
14 
15 

• 

FINDING  THE  PROFIT  OR  LOSS  ON  EACH  SALE      419 

The  numbers  of  the  departments  are  stated  at  the  head  of  the 
blank.  The  numbers  of  the  articles  in  the  departments  are  stated 
at  the  left.  Each  article  is  given  a  stock  number  when  it  is 
purchased. 

The  first  figure  of  the  stock  number  indicates  the  department ; 
the  remaining  figures  of  the  stock  number  indicate  the  number  of 
the  article  in  the  department.  For  example,  the  third  article  pur- 
chased for  Dept.  I  is  given  the  number  13,  meaning  department  1, 
number  3. 

When  an  article  is  purchased,  the  cost  clerk  adds  to  the  whole- 
sale cost  a  share  of  the  buying  and  selling  expenses  of  the  depart- 
ment, and  enters  this  total  in  the  proper  place  in  the  cost  book. 

Written  Work 

You  are  now  to  prepare  a  cost  book  for  articles  purchased  for 
six  different  departments.  You  will  be  told  the  prime  cost  of 
each  article  purchased.  The  per  cent  of  the  prime  cost  required 
to  cover  buying  and  selling  expenses  in  each  department  was 
found  in  the  preceding  exercise.  Multiply  the  prime  cost  by  the 
proper  per  cent  to  determine  the  share  of  expenses ;  add  this  to 
the  prime  cost,  and  enter  the  total  in  the  cost  book. 

Example.  The  prime  cost  of  the  first  article  purchased  for 
Dept.  I  is  ^  3.90.  What  cost  should  be  entered  in  the  cost 
book  ? 

Solution.    $  3.90    Prime  cost 

.20     To  cover  buying  and  selling  expenses  in  Dept.  I 
.78     Expenses  to  be  added 

$  3.90     Prime  cost 

.78    Expenses 
$  4.68     Total  cost  to  buy  and  sell 

Prepare  a  cost  book  for  the  following  purchases,  using  the  per 
cent  of  buying  and  selling  expenses  for  each  department  found  in 
the  exercise  on  page  418. 

Prime  cost  of  purchases:  (The  numbers  of  the  articles  are 
stated  first;  then  the  prime  costs.)  The  items  are  given  in  the 
order  of  their  purchase  from  left  to  right. 


420      FINDING  THE  PROFIT  OR  LOSS  ON  EACH  SALE 


31,122.18 

;     21, 

$  16.42 ; 

51, 

12.40; 

11,13.90; 

22, 

136.27 

12, 

4.25 

23, 

45.32; 

32, 

4.23; 

61,  12.90; 

52, 

3.90 

13, 

9.18 

.      41, 

12.46; 

62, 

18.75; 

24,27.19; 

33, 

19.27 

42, 

9.13. 

53, 

2.85; 

63, 

15.30; 

25,  36.14; 

34, 

2.30 

43, 

2.56 

,      14, 

2.32; 

54, 

6.23; 

44,    5.80; 

26, 

27.23 

64, 

23.95 

,      15, 

13.50; 

35, 

4.67; 

16,17.60; 

36, 

2.13 

45, 

4.50 

,      ^5. 

2.19; 

56, 

9.29; 

17,  13.47 ; 

37, 

4.23 

18, 

9.28 

57, 

4.80; 

58, 

2.65; 

65,26.80; 

19, 

4.62 

6Q, 

13.86. 

Save  your  results  for  future  use. 

352.  Work  of  the  Profit  Clerk.  In  stores  where  a  cost  book  is 
kept,  it  is  the  duty  of  the  profit  clerk  to  compute  the  profit  or 
loss  on  each  sale.  The  profit  clerk  is  provided  with  a  copy  of  the 
cost  book,  and  a  duplicate  of  each  invoice  of  goods  sold. 

He  finds  the  selling  price  on  the  invoice,  and  the  cost  from  the 
cost  book ;  by  subtraction,  he  is  able  to  compute  the  profit  or  loss 
on  each  sale. 

Written  Work 

Use  the  cost  book  prepared  in  the  preceding  written  exercises 
to  find  the  profit  or  loss  on  each  of  the  following  sales  : 
■1.    Invoice  No.  2345.  2.    Invoice  No.  2346. 


Selling 
Price 

6  No.  17  116.45. 

2  No.  35    5.80. 

8  No.  5Q       12.00. 
3.  Invoice  No.  2347. 

12  No.  58  $  3.26. 
10  No.  13   11.00. 

8  No.  36    2.70. 

24  No.  41       16.00. 
Less  a  cash  discount  of  1  %. 
5.    Invoice  No.  2349. 

10  No.  26  $33.50. 

5  No.  22  50.00. 

18  No.  21  22.50. 

25  No.  58  3.25. 


Selling 
Price 

■  5  No.  52  I  4.75. 

6  No.  63  19.00. 

12  No.  32  5.00. 

4.  Invoice  No.  2348. 

1  No.  61  $16.30. 

15  No.  63  19.00. 

12  No.  44  8.00. 

20  No.  45  6.00. 

6.  Invoice  No.  2350. 

20  No.  15  116.50. 
20  No.  13  12.00. 
30  No.  12    5.00. 


CHAPTER   XLV 

FACTORY  COSTS 

During  recent  years  an  increasing  interest  has  been  shown 
by  manufacturers  in  the  subject  of  cost  records  and  accounting. 
While  the  system  of  factory  cost  records  is  very  complex,  the 
fundamental  principles  are  simple. 

353.  Elements  of  Cost.  Factories  usually  divide  their  expenses, 
or  "  costs,"  into  four  classes,  namely,  direct  labor,  direct  material, 
indirect  expenses  or  manufacturing  expenses,  and  selling  expenses. 

Direct  Labor  is  labor  employed  directly  in  the  production  of  an 
article.  This  item  is  found  from  the  pay  roll  and  the  time  tickets 
of  workmen. 

Direct  Material  costs  include  all  outlays  of  materials  used  in  the 
making  of  an  article,  entering  into  and  becoming  a  part  of  it. 

Indirect  Expenses,  often  called  burden  or  overhead  expenses,  or 
manufacturing  expenses  consist  of  all  the  other  expenses  incurred 
in  the  manufacture  (but  not  the  sale)  of  the  product. 

Indirect  expenses  include  such  items  as  rent,  taxes  on  factory, 
insurance,  interest  on  factory  and  equipment  (some  accountants 
and  efficiency  experts  object  to  including  interest  as  an  expense), 
heat,  light  and  power,  repairs,  depreciation.  Indirect  labor,  in- 
cludes salaries  of  factory  superintendents  and  foremen;  wages 
of  all  men  employed  in  the  factory  at  other  than  direct  labor  on 
the  product,  such  as  janitors,  watchmen,  and  messengers. 

Selling  Expenses  include  all  expenses  incurred  in  marketing 
the  product,  such  as  advertising,  salaries,  and  expenses  of  salesmen. 

The  various  costs  are  grouped  as  follows : 

Labor  -h  Material  =  Prime  Cost. 

Prime  Cost  +  Indirect  Expenses  =  Cost  to  Make  (factory  cost). 

Factory  Cost  +  Selling  Expenses  =  Total  Cost. 

Selling  Price  -  Total  Cost  =  Profit. 

421 


422  FACTORY  COSTS 

Example.     What  are  the  costs  and  the  profit  of  a  factory,  the 


cords  of  which  show  the  following  : 

Labor, 

133,286.45 

Materials, 

$18,973.98 

Indirect  expenses. 

$15,471.25 

Selling  expenses. 

$  4,726.35 

Sales, 

192,487.50 

Solution.              Labor 

133,286.45 

Materials 

18,973.98 

Prime  cost 

^52,260.43 

Prime  cost 

$52,260.43 

Indirect  expenses 

15,471.25 

Factory  cost 

$67,731.68 

Sales 

$92,487.50 

Factory  cost 

67,731.68 

Gross  profit  on  sales 

24,755.82 

Gross  profit  on  sales 

$24,755.82 

Selling  expenses 

4,726.35 

Net  profit  on  sales 

$20,029.47 

354.  Finding  the  Profit  or  Loss  on  Each  Article.  A  manufac- 
turer can  determine  with  little  difficulty  his  total  costs  and  his 
profit,  but  it  is  more  difficult  to  determine  the  exact  cost  of  manu- 
facturing any  particular  article,  and  the  profit  or  loss  arising  from 
its  sale.  However,  it  is  very  important  for  the  manufacturer  to 
be  able  to  do  this,  because,  while  the  business  as  a  whole  may 
make  a  profit,  many  individual  articles  may  be  sold  at  a  loss.  It 
is  highly  desirable  to  know  what  all  articles  cost. 

To  find  the  factory  cost  of  an  article,  the  manufacturer  must 
know : 

a.    The  cost  of  the  labor  spent  upon  it ; 

h.    The  cost  of  the  materials  entering  into  it; 

c.  The  share  of  the  indirect  expenses  or  burden  which  should 
be  charged  to  it. 

The  records  which  show  these  facts,  are  called  "  cost  records." 

355.  Cost  Records  Illustrated.  Printing  offices  usually  have 
well-established  cost  systems,  and  we  can  illustrate  the  method 


FACTORY  COSTS 


423 


by  following  a  job  through  such  an  office.  An  order  for  5000 
letter  heads  is  sent  to  the  printing  office.  A  cost  card  is  made 
out  in  the  office,  similar  to  the  following  illustration : 


JOB  TICKET 

Job.  No..3^'?       . 

//.  f  o  /.^ 

F«.         r^  ^.  ^^-J,^.*^^^ 

Typ-        ^2/^^     (^^^.<i/f.^A^ 

Inir            ^^/■U.aA    • 

IVrmi,^     ^^y^J^^J^Ay^^'^/^/^                \ 

COSTS 

Ubor                         $ 

Burden                      $ 

SeDbigPriee              $ 

Finding  the  Material  Cost.  When  the  paper  is  cut,  its  cost  is 
computed,  and  entered  on  the  card. 

Finding  the  Labor  Cost.  Each  workman  who  is  engaged  on 
the  job  fills  out  a  time  ticket  showing  the  number  of  hours  which 
he  spent  on  it. 


TIME  TICKET 


Workman 

Job.  No.  -sM^^ 

Operation  _^^222:^z^iZ^;^^^±i: 
Began  /    OO 


Finished  ^  /-^ 
Time       /:/S 


Rale£_^£. 


.  Amount    ¥■  ^-^ 


424  FACTORY  COSTS 

356.  Finding  the  Indirect  Expenses.  This  part  of  the  cost 
record  is  the  most  difficult  to  obtain.  Before  any  job  can  be 
charged  with  a  share  of  the  burden,  two  things  must  be  deter- 
mined.    They  are  : 

a.    The  total  indirect  expenses,  overhead  or  burden. 

h.  The  best  method  of  distributing  the  expenses  among  the 
various  articles  manufactured. 

Computing  the  Total  Indirect  Expenses.  At  the  beginning  of 
the  year,  an  estimate,  or  budget,  of  probable  expenses  is  prepared. 
It  is  similar  to  the  following : 

Interest  on  plant  and  equipment     f  500.00 
Insurance  75.00 

Heat,  light,  and  power  640.00 

Repairs  125.00 

Depreciation  300.00 

Indirect  labor  1620.40 

52)Ji;3260.40     Yearly  burden. 
162.70     Weekly  burden. 

These  items  can  be  foretold  with  comparative  accuracy  by  re- 
ferring to  the  records  of  the  previous  years.  Many  other  items 
may  be  included,  but  those  stated  will  illustrate  the  method. 

We  have  now  determined  that  the  overhead  expenses  for  the 
w^eek  are  $62.70,  and  this  amount  must  be  distributed  over  all 
the  jobs  completed  or  worked  on  during  the  week. 

The  various  methods  for  distributing  overhead  expenses  are 
discussed  on  page  437. 

Written  Work 

1.  What  is  the  weekly  burden  in  a  factory  with  the  following 
annual  overhead  expenses? 

Rent,  $420.00;  Interest  on  machinery  and  other  equipment, 
$90.00;  Insurance  on  equipment,  $12.00;  Heat  and  light, 
$285.00;  Power,  $600.00;  Repairs,  $150.00;  Depreciation, 
$25.00;  Miscellaneous,  $380.00. 

2.  Find  the  total  burden  and  the  weekly  burden  in  a  factory 
reporting  the  following : 


FACTORY  COSTS  425 

Building  cost,  $8000.00 ;  Equipment  cost,  116,500.00. 

Interest  on  invested  capital  at  5|-%. 

Taxes:  Building  valued  by  assessor  at  17500.00,  taxed  on  ^  of 
its  value  ;  Equipment  assessed  at  15000.00  ;  Tax  rate,  8  2. 68. 

Insurance:  Building  insured  at  80%  of  cost;  Equipment  in- 
sured by  a  112,000.00  policy.  Rate  on  building  and  contents, 
il.30. 

Depreciation:  4%  on  building;  12  J  %  on  machinery. 

Miscellaneous,  11865.00. 

DISTRIBUTING  THE  OVERHEAD  EXPENSES  AMONG  THE 
VARIOUS  JOBS 

Several  methods  are  in  use  for  distributing  the  burden.     The 
following  are  the  most  common : 
a.    The  Direct  Labor  Cost  Method ; 
h.    The  Direct  Labor  Hours  Method ; 

c.  The  Direct  Labor  and  Materials  Cost  Method ; 

d.  The  Department  Machine  Rate  Method. 

357.  The  Direct  Labor  Cost  Method.  When  this  method  is 
used,  the  indirect  expenses  are  distributed  among  the  various  jobs 
in  the  same  ratio  as  the  cost  of  the  labor  put  on  each  of  the  jobs. 

The  computation  is  made  as  follows : 

Divide  the  weekly  burden  by  the  total  labor  cost  for  the  week 
to  find  what  per  cent  the  burden  is  of  the  labor  cost. 

Multiply  the  labor  cost  of  each  job  by  this  per  cent  to  find  the 
burden  for  each  job. 

Example.  In  the  printing  office  with  a  weekly  burden  of 
$62.70,  the  pay  roll  for  the  week  ending  September  17  was 
$370.00.  The  labor  cost  of  job  No.  635  was  $18.50.  What 
share  of  the  weekly  burden  should  be  charged  to  job  No.  635? 

Solution.  Labor  cost  for  week  $370.00 

Weekly  burden  $62.70 

The  burden  is,  therefore,      '^      of  the  labor,  or  about  17  %. 

17  %  of  the  labor  cost  of  each  job  is  added  as  burden. 
17  %  of  $  18.50  =  %  3.15,  the  burden  on  pb  No.  635. 


426  FACTORY  COSTS 

Written  Work 

1.  If  the  annual  burden  of  a  factory  is  $3280,  what  is  the 
weekly  burden  ? 

2.  The  pay  roll  of  this  factory  for  a  week  is  f  735.60.  What 
per  cent  of  the  labor  cost  of  each  job  should  be  added  to  cover 
the  burden? 

3.  The  labor  cost  of  job  No.  1729  was  827.69.  What  amount 
of  burden  should  be  included  in  the  "cost  to  make"  ? 

4.  Annual  burden,  12150. 

Pay  roll,  week  ending  May  11,  I?  296.48. 

Labor  cost  of  job  No.  234,  164.96.     What  is  the  burden  ? 

Labor  cost  of  job  No.  235,  118.26.     What  is  the  burden  ? 

5.  Annual  burden,  §4620. 

Labor  costs  per  job,  for  week  ending  August  26. 
Job  No.  1325  I    27.69 

1326  34.19 

1327  96.41 

1328  117.12 

1329  26.14 

1330  115.86 

1331  76.90 
Total  pay  roll     $494.31 

What  charge  for  burden  should  be  added  in  the  cost  of  each 
job? 

(Find  per  cent  of  burden  approximate  to  the  nearest  even  per 
cent.) 

6.  The  cost  of  material  for  each  job  was  as  follows : 

1325    $19.80  1326     121.75  1327     $48.69 

1328     $59.74  1329     $  4.90  1330     $48.75 

1331     $27.96 
What  was  the  total  cost  to  make  each  job  ? 

7.  The  selling  expenses  have  been  found,  by  experience,  to  be 
21  %  of  the  total  cost  to  make.  What  is  the  cost  to  make  and 
sell  each  job? 


FACTORY  COSTS  .  427 

8.  The  selling  price  is  determined  by  adding  28  %  to  the  cost 
to  make.  What  is  the  selling  price  of  each  job,  and  what  is  the 
profit  ? 

358.  The  Direct  Labor  Hours  Method.  This  method  is  similar  to 
the  direct  labor  cost  method,  with  the  exception  that  the  hours  of 
labor,  instead  of  the  cost  of  labor,  are  made  the  basis  of  dis- 
tribution. 

Example.  In  the  factory  with  a  weekly  burden  of  i  62.70,  the 
total  number  of  hours  worked  by  all  direct  laborers  during  the 
week  ending  October  17  was  482.  What  burden  should  be  charged 
to  job  number  173,  on  which  32  hours  of  direct  labor  were  spent? 

Solution.     Total  burden  for  ^eek,     $  62.70 
Total  direct  labor  hours,  482 

$  62.70  -4-  482  =  1 .13,  hourly  burden. 

32     Number  of  hours  spent  on  job  number  173 
$.13     Hourly  burden 
$4.16     Burden  charged  to  job  number  173 

Written  Work 

1.  The  following  jobs  were  begun  and  completed  during  the 
week  ending  September  27. 

.Job  No.  Hours  of  Labor  Labor  Cost  Material  Cost 

2789  93  128.15  114.20 

2790  104  36.18  15.55 

2791  32  10.16  6.12 
2796                       48                        15.28  8.19 

The  total  number  of  hours  of  direct  labor  on  all  jobs  during  the 
week  was  623,  and  the  annual  burden  was  f  2591.68. 

What  was  the  hourly  burden  rate  for  the  week  ending  Septem- 
ber 27? 

What  amount  of  burden  should  be  charged  to  each  job,  and 
what  was  the  total  cost  to  make  each  job  ? 

2.  The  following  table  shows  the  figures  for  jobs  on  which 
work  was  done  during  the  week  ending  September  27,  and  which 
were  completed  during  the  week  ending  October  4. 


428  .  FACTORY  COSTS 


Hours  of 

Labor 

Fob  No. 

Week  Ending 

Sept.  27 

Week  Ending 
Oct.  4 

Labor  Cost 

Material  Cost 

2792 

19 

43 

119.40 

$   8.70 

2793 

23 

69 

28.55 

13.25 

2794 

9 

46 

17.90 

6.45 

2795 

12 

52 

19.35 

7.90 

2797 

8 

95 

35.98 

14.62 

The  total  number  of  hours  of  direct  labor  for  the  week  ending 
October  4  was  712.  What  was  the  hourly  burden  rate  for  work 
done  during  the  week  ending  October  4  ? 

What  is  the  amount  of  burden  to  be  added  to  the  cost  of  each 
job  in  the  table  above  for  work  done  during  the  week  ending 
September  27  ? 

What  is  the  amount  of  burden  to  be  added  to  the  cost  of  each 
job  in  the  table  above  for  the  work  done  during  the  week  ending 
October  4  ? 

What  is  the  total  cost  of  each  job  ? 

3.  15  %  of  the  factory  cost  is  added  to  the  cost  of  each  job 
as  an  estimate  to  cover  selling  expenses.  What  is  the  cost  to 
make  and  sell  each  job,  2789  to  2797  inclusive  ? 

4.  What  profit  or  loss  was  realized  by  selling  these  jobs  at  the 
following  prices? 


Job  No. 

Selling  Price 

Job  No. 

Selling  Pric 

2789 

$63.00 

2793 

163.00 

2790 

80.00 

2794 

30.00 

2791 

20.00 

2795 

40.00 

2792 

45.00 

2796 

38.50 

2797 

75.00 

5.  Manufacturers  who  do  not  operate  a  cost  system  frequently 
add  a  certain  per  cent  of  the  prime  cost  (material  and  labor)  to 
cover  burden,  selling  expenses,  and  profit. 

What  was  the  prime  cost  of  each  job  in  Problems  1  and  2  ? 
If  33  %  were  added  to  the  prime  cost  to  determine  selling  price, 
what  would  have  been  the  selling  price  of  each  job  ? 

6.  The  actual  cost  to  make  and  sell  each  job  was  computed  by 
the  cost  system  in  Problem  3.      Compare  these  costs  with  the 


FACTORY  COSTS  429 

selling  prices  determined  in  Problem  5,  and  find  what  profit  or 
loss  would  have  been  realized  from  the  sale  of  each  job. 

359.  Direct  Labor  and  Materials  Cost  Method.  Some  manufac- 
turers prefer  to  distribute  the  burden  among  the  various  products 
in  proportion  to  the  cost  of  both  the  labor  and  the  material  enter- 
ing into  them.  When  this  methoa  is  employed,  the  process  is  as 
follows : 

Total  labor  cost  per  week  (or  other  unit  of  time)  $  525.80 

Total  materials  cost  for  the  week  264.70 

Total  labor  and  materials  cost  $790.50 

$62.70  (weekly  burden)  -^  $790.50=  7.9  %.  Per  cent  of  labor 
and  materials  cost  to  be  added  to  each  job  as  burden. 

If  the  job  ticket,  or  cost  sheet,  shows  that  $35.00  worth  of 
material  and  $53.20  worth  of  labor  have  been  put  into  a  job,  the 
burden  would  be  computed  thus  : 

$53.20     Labor  Cost 

35.00     Materials  Cost 
$88.20     Labor  and  Materials  Cost 
7.9  %  of  $88.20  =  $6.97,  Burden. 

$53.20     Labor  Cost 
35.00     Materials  Cost 
6.97     Burden 


$95.17     Cost  to  Make 


Written  Work 


1.  If  the  weekly  burden  of  a  factory  is  $6340,  and  the  cost  of 
the  materials  and  labor  put  into  the  product  of  a  week  is  $923.70, 
what  per  cent  of  the  labor  and  materials  cost  of  each  job  must  be 
added  to  cover  burden  ?  Approximate  result  to  the  nearest  half 
per  cent. 

2.  Labor  cost  on  job  No.  884,  $16.90  ;  materials  cost,  $13.25. 
What  is  the  burden,  determined  by  labor  and  materials  cost 
method,  using  the  per  cent  found  in  the  first  problem  ? 


430  FACTORY  COSTS 

3.    Complete  the  following  table. 


Annual 
Burden 

Weekly 
Burden 

Week's 
Labor 
Cost 

Week's 

Materials 

Cost 

% 

Burden 

Labor 

Cost 

One  Job 

Materials 

Cost 

One  Job 

Burden 
Per  Job 

Cost  to 

Make 

Each 

Job 

1  3145 

90 

^215 

60 

$412 

90 

1   1 

132 

15 

$  9 

75 

2268 

25 

186 

— 

45 

25 

11 » 

12 

15 

4 

70 

5496 

— 

276 

25 

396 

90 

ES^^. 

19 

25 

22 

70 

12962 

— 

893 

56 

592 

90 

-<ili 

63 

— 

49 

75 

360.  Department  Machine  Rate  Method.  The  preceding  methods 
do  not  take  into  consideration  the  fact  tliat  more  burden  should 
be  charged  for  some  operations  than  for  others. 

For  example,  let  us  suppose  that  a  factory  produces  two  kinds 
of  articles.  One  is  made  on  a  very  expensive  machine,  occupy- 
ing a  large  room,  and  requiring  a  great  deal  of  power.  The 
machine  is  delicate,  it  requires  considerable  repairing,  and  will 
wear  out  in  a  few  years.  The  depreciation,  therefore,  is  large. 
The  other  article  is  made  at  a  bench  by  hand,  and  with  cheap 
tools. 

Suppose  the  same  amount  of  material  and  labor  were  required 
to  make  each  of  these  articles.  If  any  of  the  methods  explained 
in  the  previous  sections  were  employed,  the  same  amount  of 
burden  would  be  charged  to  each  article.  But  it  is  evident 
that  the  expense  of  manufacturing  the  former  is  much  greater 
than  that  of  the  latter.  The  items  which  make  up  the  expense 
are  listed  below. 


Overhead  Expenses  of  Making 
Article  No.  1 

Interest    on    Expensive    Ma- 
chinery. 
Rent  of  Large  Room. 
Cost  of  Power. 
Repairs  on  Machinery. 
Depreciation  of  Machinery. 
Heat  and  Light. 
Incidentals. 


Overhead  Expenses  of  Making 
Article  No.  2 

Interest   on  Cheap    Bench  and 

Tools. 
Rent  of  Small  Room. 

Repairs  (very  little). 
Depreciation  (very  little). 
Heat  and  Light. 
Incidentals. 


FACTORY   COSTS 


431 


The  machine  rate  method  is  intended  to  distribute  the  burden 
in  accordance  with  the  real  expenses  of  manufacture.  The  factory 
is  divided  into  departments  or  "factors,"  similar  processes  with 
about  the  same  expenses  being  grouped  together.  The  burden  is 
then  divided  among  all  departments,  as  shown  by  the  following 
illustration. 

Suppose  that  a  factory  has  three  departments,  as  shown  by  the 
following  floor  plan 


160' 

Department  No.  1.                         50'  x  160' 

Contains  expensive  machinery 

Value  160,000.00 

Department  No.  2.     30'  x  100' 

Department  No.  3. 

30'  X  60' 

Assembling  Room 

No  equipment 

Bench  and  Tools 
Value  $1300.00 

80' 


The  burden  would  be  divided  among  the  departments  thus 


Items 

Dept.  No.  1 

Dept.  No.  2 

Dept.  No.  3 

Total 

Rent  (floor  space  160  x  80) 

Interest 

Insurance      

Heat  and  Light      .... 

Power 

Depreciation 

Supervision 

Incidentals 

$1000.00 
3000.00 
480.00 
275.00 
500.00 
1200.00 
720.00 
245.00 

$375.00 

65.00 

10.00 

130.00 

13.00 
250.00 
130.00 

$225.00 

45.00 
60.00 

175.00 
85.00 

$1600.00 

3065.00 
535.00 
465.00 
500.00 
1213.00 
1145.00 
460.00 

Total      .     . 

$7420.00 

$973.00 

$590.00 

$8983.00 

Per  week  .     .     . 

$142.69 

$18.71 

$11.35 

$172.76 

Methods  of  Distributing  Costs  among  Departments 
Rent.     The   rent    is   prorated  among   the    three   departments 


according  to  floor  space  ;  thus, 
Annual  rent  of  building",  #  1600. 


Total  floor  space,  12,800  sq.  ft. 


432  FACTORY  COSTS 

iieOO  -h  12,800  =  1.12-1,  rent  per  square  foot. 

Floor  space  Dept.  1  is  8000  sq.  ft. 

8000  X  1.12-1-  ^  11000,  Rent  Dept.  1. 

Floor  space  Dept.  2  is  3000  sq.  ft. 

3000  X  $  .121  =  1375,  Rent  Dept.  2. 

Floor  space  Dept.  3  is  1800  sq.  ft. 

1800  X  f  .121  =  1225,  Rent  Dept.  3. 

Interest.     5  %  interest  on  1 60,000  =  13000,  Int.  Dept.  1. 

5  %  interest  on  11300  =  I  65,  Int.  Dept.  2. 

Insurance.  Insurance  on  the  building  is  piJ-orated  among  the 
departments  in  proportion  to  floor  space. 

Insurance  on  equipment  is  determined  by  the  value  of  the 
equipment. 

Heat  and  Light.     Heat  is  prorated  according  to  floor  space. 

Light  may  be  prorated  b}^  floor  space,  or  a  separate  meter  may 
show  the  cost  of  the  light  used  in  each  department. 

Depreciation.  Depreciation  on  the  building  is  prorated  by  floor 
space. 

Depreciation  on  equipment  depends  upon  the  value  of  the 
equipment. 

Finding  the  Hourly  Burden  Rate  for  Each  Department.  To  apply 
this  method  of  distributing  the  burden  among  the  various  jobs,  the 
total  number  of  hours  of  labor  spent  in  each  department  for  a 
week,  or  other  period,  must  be  known.  Then  the  weekly  burden 
in  each  department  is  divided  by  the  number  of  hours  of  labor 
each  week  in  the  department,  to  determine  the  hourly  burden  rate. 

Example.  Let  us  suppose  the  total  hours  of  labor  in  each  de- 
partment for  a  certain  week  were  as  follows  : 

Dept.  No.  1,  317 ;  Dept.  No.  2,  104  ;  Dept.  No.  3,  95. 

What  was  the  hourly  burden  rate  in  each  department?" 

Solution.     Dept.  1.     $  142.69  (weekly  burden)  -317=1 .45,  hourly  rate. 
Dept.  2.     $  18.72  (weekly  burden) --  104  =  $.18,  hourly  rate. 
Dept.  3.     $  11.35  (weekly  burden)  ^  95  =  $  .12,  hourly  burden. 

Finding  the  Overhead  Expenses  and  the  Total  Cost,  when  the 
Machine  or  Department  Rate  is  Used. 

Example.  The  labor  cost  of  an  article  (made  during  the  week 
the   hourly    burden  rates   of   which  were   determined  above)  is 


FACTORY  COSTS 


433 


113.40  ;  materials  cost,  i  11.80.  The  labor  hours  in  the  different 
departments  were  as  follows  : 

Dept.  1,  28  hours  ;  Dept.  2,  5  hours  ;  Dept.  3,  8  hours. 

What  were  the  overhead  expenses  charged  to  this  job,  and 
what  was  the  total  cost  ? 

Solution. 


Labor  cost 

^13.40 

Materials  cost 

11.80 

Burden 

Dept.  1  ;  28  hours  at  |  .45 

$12.60 

Dept.  2 ;     5  hours  at     .18 

.90 

Dept.  3  ;     8  hours  at     .12 

.96 

Total  burden 

14.46 

Total  cost  to  make 

$39.66 

Written  Work 
1.    Prepare  an  estimate   of  the  annual  burden  of  the  factory 
occupying  a  building  with  the  following  floor  plan : 

Scale  i"  =  10' 


Dept.  No.  1 

Dept.  No.  2 

Dept.  No.  3 

Interest  on  Building.  The  building  cost  f  15,000.00.  5|  % 
interest  on  this  cost  is  prorated  among  the  departments  in  pro- 
portion to  the  square  feet  of  floor  space  occupied  by  each. 

Insurance  on  Building.  The  building  is  insured  at  |  of  its  cost. 
Rate,  il.65.  The  total  cost  of  the  premium  is  prorated  by  floor 
space. 

Taxes  on  Building.  The  building  is  assessed  at  ^  of  its  cost, 
and  taxed  at  $  2.90.     Tax  prorated  by  floor  space. 


434  FACTORY  COSTS 

Depreciation  of  Building.  4  %  annual  depreciation  on  the 
original  value  of  the  building  is  prorated  by  floor  space. 

Interest  on  Equipment.  Dept.  No.  1  contains  machinery  valued 
at  818,000.00. 

Dept.  No.  2  contains  benches  and  tools  valued  at  82,000.00. 

Dept.  No.  3  is  an  assembly  room  and  contains  no  machinery. 

Each  department  is  charged  5|  %  interest  on  the  value  of  its 
equipment. 

Insurance  on  Equipment.  A  8 15,000.00,  three-year,  insurance 
policy  covering  the  equipment,  cost  83.30  per  hundred.  One 
third  of  the  cost  of  this  insurance  is  charged  annually  as  an  ex- 
pense, and  is  prorated  among  the  departments  in  proportion  to  the 
value  of  the  equipment. 

Taxes  on  Equipment.  The  taxes  on  the  equipment,  8116.00,  are 
prorated  according  to  the  value  of  the  equipment.  The  tax  rate 
is  the  same  as  on  the  building. 

Depreciation.  8  %  depreciation  is  charged  on  the  machinery  in 
Dept.  No.  1 ;  4  %  depreciation  on  equipment  in  Dept.  No.  2. 

Heat  and  Light.  The  records  show  that  the  heat  and  light  bills 
for  the  three  preceding  years  were:  8625.00;  8680.00;  8  630.00. 
Find  the  average  annual  expense  and  assume  that  this  will  be  the 
expense  for  the  coming  year.     Prorate  by  floor  space. 

Power.  The  average  annual  cost  of  power  to  run  the  machinery 
is  81460.00.     Power  is  required  in  Dept.  1  only. 

Supervision.  The  salaries  of  foremen  are  charged  to  the  de- 
partments as  follows  : 

Dept.  No.  1  8865.00 
Dept.  No.  2  530.00 
Dept.  No.  3       680.00 

Incidentals.  Dept.  No.  1     8325.90 

Dept.  No.  2  280.00 
Dept.  No.  3       175.00 

2.  What  is  the  weekly  burden  in  the  factory  and  in  each 
department? 

3.  Since  the  number  of  hours  of  labor  differs  each  week,  the 
hourly  burden  will  also  differ  each  week.  Complete  the  following 
table. 


FACTORY  COSTS 


435 


Table  of  Hourly  Burden  Rates 


Drpaktment  No.  1 

Department  No.  2 

Department  No.  3 

Labor 
Hours 

Hourly 
Burden 

Labor 
Hours 

Hourly 
Burden 

Labor 
Hours 

Hourly 
Burden 

April  4 
April  11 
April  18 
April  25 
May  2 

460 
495 
480 
395 
409 

244 

285 
260 
203 
221 

148 
163 
157 
130 
142 

Approximate  results  to  the  nearest  cent. 

4.  The  following  table  shows  the  number  of  labor  hours  in  each 
of  three  departments  spent  on  job  No.  493,  and  also  the  labor  cost 
of  the  job.  Labor  Hours  and  Cost  Order  No.  493 


Date 

Work- 
man 

No, 

Hours 

Bate 

Wages 

Department  1 

Department  2 

Department  3 

April 

2 

16 

9 

.36 

^3 

24 

3 

16 

7 

.36 

2 

52 

23 

9 

.29 

2 

61 

4 

6 

16 
23 

5 

.36 

.29 

1 
1 

80 

30 

6 

74 

7 

28 

9 

.24 

2 

16 

10 

28 

6 

.24 

1 

44 

21 

8 

.25 

2 

00 

11 
13 

28 
16 

7 

.24 

.36 

1 

1 

68 

14 

22 

4 

44 

14 

28 

5 

.24 

1 

20 

• 

15 

21 

8 

.25 

2 

00 

16 

31 

7 

.38 

2 

66 

12 

5 

7 

$26 

49 

The  materials  cost  of  job  No.  493  w^as  $13.75. 

The  burden  was  computed  as  follows : 

The  total  number  of  hours  of  labor  per  week  in  each  department 
was  determined;  the  number  of  hours  of  labor  in  each  depart- 
ment was  multiplied  by  the  hourly  burden  rate  for  the  respective 


436 


FACTORY  COSTS 


weeks.     (The  rates  used  in  this  illustration  are  not  the  same  as 
those  in  the  completed  table  on  page  435.) 

Cost  Sheet  Order  No.  493 


Week 
Ending 

Dept. 
No. 

Ilorus 

Kate 

Amount 

Summary 

April    4 

1 

30 

26.9 

$8 

07 

Labor              $26 

49 

11 

1 

14 

28.4 

3 

98 

Material            13 

75 

2 

22 

10.6 

2 

33 

Burden               19 

28 

18 

1 

12 

27.8 

3 

34 

Total         $59 

52 

2 
3 

5 

7 

11.3 
14.2 

57 
99 

$19 

28 

The  labor  cost  is  what  per  cent  of  the  total  cost  ? 
The  materials  cost  is  what  per  cent  of  the  total  cost  ? 
The  burden  is  what  per  cent  of  the  total  cost  ? 
5.    Rule  a  cost  sheet  and  find  the  total  cost  of  order  No.  494. 
Use  the  weekly  burden  rates  found  in  the  table  on  page  435. 


Materials  Cost,  $18.83 
Labor 


Order  No.  494 


Workman 

No. 

Hours 

Dept.  I 

Dept.  II 

Dept.  Ill 

April    3 

April    4 

April    4 

April-  6 

April    6 

April    8 

April    8 

April    9 

April    9 

April  13 

April  13 

April  15 

April  15 

April  15 

April  16 

April  16 

27 
27 
42 
27 
42 
27 
42 
27 
42 
27 
42 
27 
42 
61 
42 
61 

6 
9 

8 

5 

6 

4 

2 

4 

9 
3 

7 
8 
9 
2 

0 

7 

.35 
.35 
.32 
.35 
.32 
.35 
.32 
.85 
.32 
.35 
.32 
.35 
.32 
.39 
.32 
.39 

FACTORY  COSTS  437 

6.  Labor  cost  is  what  per  cent  of  total  cost  to  make  ? 
Materials  cost  is  what  per  cent  of  total  cost  to  make  ? 
Burden  cost  is  what  per  cent  of  total  cost  to  make  ? 

7.  If  6  %  is  added  to  the  cost  to  make,  to  cover  selling  ex- 
penses, what  is  the  cost  to  make  and  sell  ? 

8.  What  must  the  selling  price  be  to  make  a  profit  of  16|  %  on 
the  cost  to  make  ? 


CHAPTER   XLVI 
TABULATIONS   FOR  THE   SALES   MANAGER 

Business  men  who  are  conducting  large  enterprises  realize  the 
importance  of  having  carefully  prepared  statistics  showing  the 
results  of  their  past  activities,  in  order  to  judge  the  wisdom  of 
their  policies  and  to  assist  them  in  planning  for  the  future. 

361.  Duties  of  the  Sales  Manager.  The  sales  manager  is  ex- 
pected to  increase  the  volume  of  business.  In  order  to  accomplish 
this,  he  must  know  the  sales  of  each  clerk,  and  of  each  depart- 
ment. When  he  has  this  information,  he  is  in  a  position  to  com- 
pare the  efficiency  of  his  clerks.  The  facts  which  he  will  be  able 
to  obtain  from  such  tabulations  as  are  illustrated  in  this  chapter 
will  enable  him  to  manage  his  work  more  efficiently. 

362.  Individual  Daily  Sales  Sheet.  On  the  form  below  there  are 
entered  the  sales  of  one  day  in  one  department  of  a  store. 

If  a  clerk  on  some  preceding  day  sold  a  customer  an  article  which 
the  customer  returned,  the  clerk's  profit  to  the  store  is  thereby 
decreased.  Returned  sales  are,  therefore,  entered  in  the  second 
column,  and  deducted  from  the  gross  sales  to  determine  net 
sales. 

In  the  last  column  is  entered  the  number  of  checks,  or  sales 
tickets,  made  out  by  each  clerk  during  the  day.  Record  is  made 
of  the  checks  in  order  to  determine  the  number  of  sales  made  by 
each  clerk.  The  daily  sales  may  have  been  small,  but  the  clerk 
may  have  served  a  large  number  of  customers. 

Of  what  value  would  this  blank  be  to  the  sales  manager  ? 

Written  Work 

Prepare  a  daily  sales  sheet  from  the  following : 

438 


TABULATIONS  FOR  THE  SALES  MANAGER  439 

Individual  Daily  Sales  Sheet 
Spfif,ir>Ti    ^Q-  ^5  =  Dress  Goods Date        5/2/17 jg 


Cleek's 
Number 

Gross  Sales 

Returned  Goods 

Net  Sales 

Checks 

4501 

287 

96 

113 

02 

314 

39 

128 

03 

136 

32 

4 

92 

84 

04 

315 

26 

12 

25 

115 

05 

503 

16 

121 

06 

263 

50 

1 

25 

103 

07 

98 

30 

2 

80 

67 

08 

193 

50 

123 

09 

215 

67 

3 

96 

89 

10 

309 

50 

15 

75 

131 

11 

235 

80 

26 

15 

98 

12 

96 

15 

35 

13 

103 

28 

5 

60 

65 

14 

128 

95 

82 

15 

202 

75 

3 

10 

96 

16 

127 

30 

60 

Total 

363.  Salesman's  Cumulative  Tabulation.  This  blank  is  used  to 
record  the  sales  of  a  traveling  salesman  who  sells  the  goods  of 
several  departments.  Each  month  his  sales  are  entered  by  depart- 
ments in  the  proper  column.  After  the  January  and  February 
sales  are  entered,  the  amounts  for  the  two  months  are  cumulated ; 
that  is,  added.  As  each  month's  sales  are  entered  they  are 
cumulated  with  the  preceding  total.  Thus,  at  any  time  during  the 
year,  this  blank  shows  the  following  facts  : 

The  salesman's  sales  per  month  in  each  department ; 

His  total  sales  to  date  in  each  department ; 

His  total  sales  each  month  in  all  departments ; 

His  total  sales  in  all  departments. 

Written  Work 
Prepare  a  cumulative  sales  report  for  Salesman  No.  32. 
Find  the  total  sales  per  month. 
Cumulate  the  sales  as  indicated  on  the  form  on  page  440. 


440 


TABULATIONS  FOR  THE  SALES  MANAGER 


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TABULATIONS  FOR  THE  SALES  MANAGER 


441 


364.  Monthly  Percentage  Comparison  of  Salesmen.  Sales  mana- 
gers consider  it  very  important  to  have  comparisons  of  their 
different  salesmen.  They  wish  to  know  not  only  the  amount  of 
the  sales  made  by  each,  but  also  what  fractional  part  of  the  total 
sales  was  sold  by  each.  The  most  convenient  way  to  state  these 
fractions  is  by  percentage. 

Written  Work 

Prepare  a  form  similar  to  the  one  indicated  in  the  following 
illustration : 

Monthly  Comparison  of  Salesmen 


Salesman's 
No. 

First 
Week 

Second 
Week 

Third 
Week 

fottrtii 
Week 

Fifth 
Week 

Total 

Per  Cent 

I 

$320.70 

$230.49 

$563.40 

$834.70 

$123.70 

II 

470.65 

870.43 

933.60 

274.80 

85.70 

III 

376.80 

543.70 

625.80 

735.43 

137.89 

IV 

339.40 

763.35 

347.84 

347.96 

99.89 

V 

276.80 

563.90 

743.90 

876.90 

470.96 

VI 

723.96 

439.65 

375.63 

648.93 

275.93 

VII 

374.99 

687.93 

684.96 

532.89 

99.64 

VIII 

268.37 

536.96 

648.97 

374.88 

63.96 

IX 

469.89 

746.93 

387.93 

479.69 

364.84 

X 

479.89 

489.89 

683.89 

874.96 

216.80 

XI 

376.86 

375.94 

632.61 

276.93 

-  39.96 

XII 

546.64 

789.94 

346.49 

832.24 

162.27 

XIII 

345.49 

328.84 

769.94 

962.63 

137.90 

XIV 

476.63 

374.84 

265.89 

649.84 

202.03 

XV 

763.47 

239.84 

646.63 

389  84 

62.99 

Totals 

Enter  the  sales  in  the  proper  columns. 

Find  the  total  sales  made  each  week  by  all  salesmen.  These 
totals  should  be  entered  at  the  foot  of  the  columns. 

Find  the  total  sales  made  by  each  salesman  during  the  month. 
This  will  require  horizontal  addition,  and  the  totals  should  appear 
in  the  "  Total "  column  at  the  right. 

Find  the  grand  total  sales  for  the  month.  (As  a  means  of 
checking  your  work,   find  the  grand  total  in  two  ways:  (a)  by 


442  TABULATIONS  FOR  THE  SALES  MANAGER 

adding  the  totals  at  the  foot  of  the  blank,  and  (6)  by  comparing 
this  result  with  the  total  of  the  "  Total "  column  at  the  right. 

Find  what  per  cent  of  the  grand  total  sales  was  made  by  each 
salesman.     Enter  these  per  cents  in  the  column  at  the  right. 

365.  Comparisons  with  Previous  Year.  Business  men  are  inter- 
ested in  the  growth  of  their  sales,  profits,  etc.,  and  make  frequent 
use  of  comparative  tables  which  bring  out  clearly  the  increase 
or  decrease  in  the  business.  In  addition  to  recording  each 
salesman's  sales  by  weeks,  months,  and  cumulatively,  and  in 
addition  to  comparing  the  records  of  different  salesmen  to  deter- 
mine their  comparative  efficiency  as  shown  by  their  per  cent  of 
sales,  the  office  often  prepares  a  record  of  each  salesman's  sales  for 
the  current  year  as  compared  with  his  sales  of  the  preceding  year, 
to  show  the  amount  of  increase  or  decrease,  and  also  the  per  cent 
of  increase  or  decrease. 

Written  Work 

Enter  the  following  information  on  a  properly  ruled  form. 
Find  the  yearly  totals,  the  increase  or  decrease  in  dollars,  and  also 
in  per  cents. 

Finding  the  Per  Cent  of  Increase  or  Decrease.  First  express  the 
increase  or  decrease  over  the  previous  year  as  a  fraction^  using  as 
the  numerator  the  increase  or  decrease^  and  as  the  denominator^  the 
previous  years  sales.     Change  this  common  fraction  to  a  per  cent. 

Example.  What  is  the  per  cent  of  increase  in  a  business  that 
yields,  respectively,  $3000  and  83600  in  two  successive  years? 

Solution.     This  year's  sales  for  January $3600 

Last  year's  sales  for  January 3000 

Increase 600 

Fraction  showing  increase  over  last  year 

^  ^  3000 

Changed  to  per  cent  =  20  %. 

From  this  tabulation  the  sales  manager  can  determine  the  sales- 
men whose  efficiency  is  increasing,  and  can  reward  them  by  in- 
creased salary. 


TABULATIONS  FOR  THE  SALES  MANAGER 


443 


Chart  Showing  Increase  or  Decrease  of  Sales 

Name 


Month 

Sales 
Last  Year 

Sales 
This  Yeab 

Inckease 

Per  Cent 
Increase 

Decrease 

Per  Cent 
Decrease 

January    .... 

$346 

29 

$427 

95 

February 

. 

457 

75 

515 

86 

March 

385 

86 

395 

57 

April   .     . 

416'87 

402 

75 

May     .     . 

29584 

312 

75 

June    .     . 

212 

67 

235 

84 

July     .     . 

416 

47 

493 

75 

August     . 

328 

57 

319 

56 

September 

425 

65 

483 

75 

October    . 

513 

86 

603 

52 

November 

627 

94 

673 

49 

December 

743 

85 

623 

57 

Total     . 

366.  Salesman's  Record  of  Comparative  Sales  and  Profits  by 
Departments.  The  following  form  is  somewhat  similar  to  the  form 
on  page  441.  This  form,  however,  compares  the  profits  of  one  year 
with  the  profits  of  the  preceding  year.  This  traveling  salesman  sells 
goods  in  ten  departments.  The  profits  from  his  sales  are  computed 
by  the  profit  clerk,  and  his  total  profits  by  departments  are 
entered  on  the  record. 


Written  Work 

Prepare  a  record  of  comparative  sales  and  profits  for  the  sales 
of  E.  H.  Barlow. 

Find  the  total  sales  and  the  total  profits  for  each  year. 

The  profits  were  what  per  cent  of  the  sales  in  each  depart- 
ment ? 

After  the  per  cent  of  profit  in  each  department  for  the  two 
years  has  been  determined,  the  increase  or  decrease  in  the  per  cent 
of  profit  can  be  found  by  subtraction.  Enter  increases  in  black 
ink,  and  decreases  in  red  ink. 


444 


TABULATIONS  FOR  THE  SALES  MANAGER 


Salesman's  Record  of  Comparative  Sales  by  Departments 
Salesman's  Name  —  E.  H.  Barlow 


Dbpt. 

1917 

1918 

Per  Cent 
Decrkase 
Increasb 

Sales 

Profits 

Per 
Cent 

Sales 

Profits 

Per 
Cent 

I 

II 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

$12162.40 
3147.90 

14127.65 
3287.96 
5372.47 
6392.49 

15271.34 

896.29 

1247.89 

13467.47 

$  1456.80 

629.60 

1732.86 

362.80 

437.89 

326.80 

1376.45 

46.86 

97.62 

1263.43 

$13162.90 
3319.80 

15216.90 
3347.80 
5629.90 
5146.79 

15423.66 
1989.60 
1462.96 

14362.62 

$  1562.80 
640.90 

1927.90 
367.90 
469.90 
294.90 

1389.90 

66.80 

103.60 

1346.90 

Total 

367.  Daily  Classification  of  Sales  by  Departments.  The  tabula- 
tion described  in  this  section  shows  the  daily  sales  in  each  depart- 
ment, the  total  daily  sales  in  the  entire  store,  and  the  total  sales 
of  each  department  for  the  week. 


Weekly  Classification  of  Sales  by  Departments 


Dept. 

Monday 

I'UESDAV 

Wednes- 
day 

TlIURSDA\ 

Friday 

Saturday- 

Total 

I 

II 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

> 

Total 

Per  Cent 

TABULATIONS  FOR  THE  SALES  MANAGER 


445 


The  per  cent  column  at  the  bottom  shows  what  per  cent  of  the 
week's  total  sales  was  made  each  day. 

The  per  cent  column  at  the  right  shows  what  per  cent  of  the 
week's  total  sales  was  made  in  each  department. 

Written  Work 

Prepare  a  form  similar  to  the  illustration.  Enter  the  following 
facts  on  the  form. 


Dept. 

Monday 

Tuesday 

Wednesday 

Thursday 

Friday 

Saturday 

I 

11213.85 

$1194.83 

$  949.37 

$1384.39 

$1029.47 

$1593.48 

II 

1023.75 

1094.82 

1127.49 

1284.29 

974.92 

1326.83 

III 

1125.94 

1183.27 

1248.48 

1494.84 

827.84 

1426.46 

IV 

923.85 

1184.37 

1395.47 

1029.84 

831.15 

1285.31 

V 

2539.75 

1823.57 

1531.84 

1925.29 

2041.73 

2848.57 

VI 

1925.85 

1482.16 

1632.83 

1451.61 

1348.41 

2154.38 

VII 

1594.85 

1238.57 

1285  94 

923.74 

1128.48 

1328.94 

VIII 

1923.84 

1528.49 

1228.47 

1395.47 

1463.94 

1927.47 

IX 

2594.48 

2049.47 

1829.46 

1739.84 

1832.47 

2885.81 

X 

1523.82 

1449.82 

1327.46 

1554.53 

1232.84 

1723.49 

Find  the  total  sales  for  each  day. 

Find  the  total  sales  for  the  week  in  each  department. 

Find  the  total  sales  made  by  the  store  during  the  week. 

On  the  bottom  line,  show  what  per  cent  of  the  week's  sales  was 
made  each  day. 

In  the  column  at  the  right,  show  what  per  cent  of  the  week's 
sales  was  made  in  each  department. 

Plot  a  curve  on  graphically  ruled  paper,  showing  the  total  sales 
made  in  the  store  each  day  of  the  week. 

From  this  form  and  the  graph,  the  sales  manager  can  determine 
which  days  had  the  lowest  sales  and  he  will  probably  offer  extra 
bargains  on  those  days  in  order  to  attract  more  customers.  He 
will  also  be  able  to  locate  the  departments  with  the  smallest  per 
cent  of  sales,  and  will  take  measures  to  increase  the  trade  in  those 
departments. 


446 


TABULATIONS  FOR  THE  SALES  MANAGER 


368.  Yearly  Sales  by  Months  in  All  Departments.  The  form 
illustrated  in  this  exercise  shows  the  total  sales  per  month  in  each 
department  of  a  store.  It  furnishes  the  basis  for  various  compari- 
sons ;  for  illustration,  the  gross  sales  by  departments  can  be  com- 
pared either  by  months  or  for  the  entire  year.  A  graph  could 
easily  be  prepared  from  this  table,  showing  the  variation  of 
monthly  sales  in  each  department. 

Written  Work 

Prepare  a  table  from  the  following  information.  Find  the 
annual  sales  in  each  department ;  find  the  total  sales  each  month 
for  the  entire  store. 


Dept.  I 

Dept.  II 

Dept.  Ill 

Dept.  IV 

Dept.  V 

Total 

January 

.     11238.95 

$3728.94 

15238.64 

$2927.46 

$6223.58 

February 

.       1136.95 

3927.47 

5329.47 

2842.14 

6128.47 

March  . 

.       1145.98 

4023.45 

5183.92 

2812.51 

5923.74 

April    . 

.       1032.84 

3925.36 

5023.94 

2642.23 

5414.42 

May     . 

947.83 

3723.75 

4823.46 

2523.95 

5324.94 

June     . 

923.45 

3582.45 

4213.27 

2348.41 

5942.38 

July      . 

1123.76 

3327.74 

3928.48 

2493.48 

5283.85 

August     . 

946.73 

3527.94 

3215.13 

2493.15 

5328.47 

Septembei 

982.67 

3628.94 

3921.14 

2532.57 

•    5623.95 

October 

1095.85 

3825.93 

4428.48 

2724.71 

5923.42 

Novembei 

'       1123.86 

3927.85 

4913.73 

3124.93 

6113.81 

Decerabei 

•       1357.94 

4129.54 

5492.14 

3295.58 

6395.73 

Plot  a  curve  on  graphically  ruled  paper,  showing  the  variations 
in  monthly  sales  in  Department  I. 

369.  Sales  and  Returned  Goods  by  Departments.  The  form 
illustrated  on  page  447  shows  the  annual  sales  in  each  depart- 
ment, the  goods  returned  by  customers  to  each  department,  the 
net  sales,  and  the  per  cent  of  sales  returned  to  each  department. 


Written  Work 
Prepare  a  form  similar  to  the  model. 


TABULATIONS  FOR  THE  SALES  MANAGER 


447 


Enter  the  following  facts  : 

Dept.  I,  Sales,  f  27,493.75;  Returns,  8823.85.  Dept.  II,  Sales, 
154,294.74;  Returns,  $924.74.  Dept.  Ill,  Sales,  $82,583.84; 
Returns,  $1239.36.  Dept.  IV,  Sales,  $107,239.75;  Returns, 
$1257.34.  Dept.  V,  Sales,  $85,294.63;  Returns,  $923.75. 
Dept.  VI,  Sales,  $112,437.85;  Returns,  $723.74.  Dept.  VII, 
Sales,  $82,374.50  ;   Returns,  $1328.85. 


Dept. 

Sales 

Eetttkned  Goods 

Net  Sale 

Per  Cent  of 

Sales 

Returned 

Total .     .     . 

Find  the  net  sales  for  each  department,  the  per  cent  of  sales 
returned  to  each  department,  the  total  sales  for  the  year,  the 
total  amount  of  goods  returned  to  all  departments  during  the 
year,  the  net  sales  for  the  year,  and  the  per  cent  of  sales  returned 
to  the  store  during  the  year. 

Show  by  a  curve  plotted  on  graphically  ruled  paper,  the  per  cent 
of  sales  returned  to  each  department. 

370.  Sales  Classified  by  Days  and  Departments.  The  form  on 
page  448  shows  the  daily  sales  for  one  week  in  twenty-five  selling 
sections.  (Each  department  may  be  subdivided  into  several  sell- 
ing sections  ;  for  example,  the  men's  clothing  department  into 
sections  for  suits,  overcoats,  hats,  etc.) 

Written  Work 

Prepare  a  classification  of  sales  by  days  and  by  departments. 

Enter  the  amounts  in  the  proper  column  ;  find  the  total  sales 
for  each  day,  and  for  each  section.  Also  find  the  grand  total 
sales.     Be  sure  that  this  grand  total  checks  all  additions. 


448 


TABULATIONS  FOR  THE  SALES  MANAGER 


Sales  Classified  by  Days  and  by  Departments 


Dept. 

Monday 

Tuesday 

Wednesday 

TUUKSDAY 

Friday 

Saturday 

Total 

1 

$423.60 

$187.47 

$279.19 

$789.01 

$203.94 

$101.97 

2 

543.54 

632.65 

443.22 

339.75 

365.93 

234.56 

3 

100.10 

999.99 

203.82 

901.09 

584.85 

475.86 

4 

594.32 

567.98 

213.45 

191.12 

218.12 

345.09 

5 

555.33 

224.60  • 

100.00 

201.35 

857.02 

905.43 

6 

504.60 

543.52 

421.05 

164.30 

305.34 

465.89 

7 

102.93 

621.19 

178.92 

630.95 

304.89 

985.64 

8 

567.23 

324.54 

858.87 

664.88 

234.98 

876.32 

9 

908.23 

765.54 

510.25 

654.21 

894.32 

564.32 

10 

809.32 

432.66 

141.15 

234.65 

124.56 

784.32 

11 

239.08 

111.03 

400.00 

191.31 

123.45 

621.31 

12 

178.92 

543.98 

753.60 

555.33 

135.62 

152.02 

13 

164.30 

324.98 

827.26 

578.98 

113.56 

105.15 

14 

594.32 

234.65 

252.42 

421.05 

211.31 

202.01 

15 

339.75 

432.66 

323.23 

213.45 

135.62 

615.20 

16 

911.26 

234.56 

789.02 

512.12 

218.21 

201.51 

17 

345.67 

890.23 

456.78 

518.29 

14L19 

520.20 

18 

902.34 

567.89 

589.13 

234.13 

720.95 

111.11 

19 

979.15 

860.17 

762.95 

729.84 

789.01 

33.33 

20 

519.79 

790.11 

825.85 

678.11 

101.97 

754.46 

21 

200.20 

996.57 

908.23 

456.34 

656.54 

644.57 

22 

987.87 

100.98 

819.38 

517.83 

671.78 

135.76 

23 

112.34 

567.67 

450.78 

189.58 

150.85 

200.43 

24 

109.32 

528.49 

246.18 

ISO.81 

917.99 

774.82 

25 

933.47 

467.83 

239.08 

652  29 

493.86 

496.73 

Total 

371.  Daily  Sales  Compared  with  Sales  of  Corresponding  Day  of 
Preceding  Year.  One  of  the  most  common  methods  of  noting  the 
growth  of  a  business  is  to  compare  the  sales  of  each  day  with  the 
sales  of  the  corresponding  day  of  the  preceding  year.  It  is  as- 
sumed that  trade  conditions  will  be  about  the  same,  year  after  year, 
at  the  same  time  of  the  year.  By  comparing  the  sales  of  the  first 
Monday  in  October,  1917,  with  the  sales  of  the  first  Monday  in 
October,  1916,  a  basis  of  comparison  is  furnished  to  show  increase 
or  decrease  in  business.    It  is  customary  to  enter  on  the  blank  the 


TABULATIONS  FOR  THE  SALES  MANAGER 


449 


weather  conditions  for  the  two  days,  since  the  weather  would 
affect  the  volume  of  sales. 

Written  Work 

Prepare  a  blank  similar  to  the  model. 
Enter  the  following  facts  on  the  form. 

Daily  Sales  Report  by  Selling  Sections 
Aug.  2,  1917 


Section  No. 

This  Year 

Last  Year 

Increase 

Per 

Cent 

Decrease 

Per 
Cent 

1 

$619.20 

$603.60 

2 

85.70 

90.21 

3 

214.00 

196.80 

4 

716.26 

654.30 

5 

426.80 

397.80 

6 

562.70 

571.32 

7 

627.80 

503.60 

8 

462.80 

403.40 

9 

1037.90 

862.40 

10 

729.60 

642.80 

. 

11 

327.96 

417.84 

12 

526.94 

327.64 

13 

827.83 

941.62 

14 

987.60 

864.95 

15 

479.90 

532.60 

16 

362.85 

325.90 

17 

762.35 

629  89 

- 

18 

236.80 

329.40 

19 

246.89 

639.90 

20 

427.86 

547.77 

21 

572.96 

563.84 

22 

294.84 

289.77 

23 

276.89 

286.89 

24 

347.80 

329.99 

25 

532.87 

531.39 

26 

274.79 

239.80 

Total 

Find  the  increase  or  decrease,  and  the  per  cent  of  increase  or 
decrease,  in  the  sales  for  each  selling  section,  and  for  the  entire 
department. 


450 


TABULATIONS   FOR  THE  SALES  MANAGER 


372.  Form  Showing  the  Per  Cent  of  the  Stock  on  Hand  at  the  Be- 
ginning of  the  Month  Sold  during  the  Month.  The  following  form 
shows  what  per  cent  of  the  stock  on  hand  at  the  beginning  of  the 
month  is  turned  during  the  month.  An  inventory  is  taken  at 
the  beginning  of  the  month,  the  sales  of  the  month  are  recorded, 
and  the  per  cent  of  the  inventory  sold  is  computed. 

Example.  The  inventory  at  the  beginning  of  January  showed 
540  suits  on  hand.  During  the  month  360  suits  were  sold.  What 
per  cent  of  the  stock  was  sold  ? 


Solution. 


f|§,  the  fraction  of  the  stock  sold. 
360  -^  540  =  66f  %. 


Written  Work 


Prepare  a  blank  similar  to  the  model. 
Enter  the  following  data. 


1916 

1917 

Month 

Stock 

Sales 

Per  Cent 

OF  Stock 

Sold 

Stock 

Sales 

Per  Cent 

OK  Stock 

Sold 

Per  Cent 
Increase 

Per  Cent 
Decrease 

Jan. 

$1864 

$1631 

87.5 

$2163 

$1731 

80.0 

7.5 

Feb. 

1632 

1437 

1973 

1562 

March 

1689 

1307 

1865 

1437 

April 

1432 

787 

1437 

986 

May 

1063 

836 

1237 

884 

June 

1773 

824 

1147 

835 

July 

1089 

829 

1312 

846 

Aug. 

1002 

786 

1562 

897 

Sept. 

1347 

965 

1575 

979 

Oct. 

1689 

1087 

1734 

1137 

Nov. 

1947 

1476 

2074 

1562 

Dec. 

2137 

1694 

2263 

1734 

Total 

Complete  the  form  by  showing  what  per  cent  of  the  stock 
on  hand  at  the  beginning  of  the  month  was  sold  during  the 
month ;  also  show  the  per  cent  of  increase  or.  decrease  the  second 
year. 


TABULATIONS  FOR  THE  SALES  MANAGER 


451 


373.  Department  Record  of  Sales,  Profits,  etc.  The  following 
table  shows  one  of  the  more  elaborate  forms  of  store  records. 

Written  Work 

Rule  a  form  similar  to  the  illustration.  Use  the  following 
data  and  complete  the  blank.  Your  ability  to  prepare  this  exer- 
cise without  further  explanation  will  be  a  good  test  of  your 
efficiency.  Prorate  the  salaries,  commissions,  and  other  expenses, 
according  to  sales. 

Department    Sales,    Gross    Profits,    Returned    Goods,   Net    Profits, 
Per  Cent  of  Net  Profits,  and  Comparison  with  Last  Year 


Dept. 

Sales 

Gross 
Profits 

■5 

1 

p4 

Prorated 
Shake  of 
Salesman's 
Salary  ani> 
Expenses 

1 

i! 

ill 

H  < 

1 

$  3465.80 

1   832.46 

$134.60 

$27.30 

7 

2 

2247.95 

629.22 

94.97 

21.13 

12 

3 

1276.96 

169.94 

4 

4 

974.44 

202.41 

15 

5 

326.87 

164.69 

21 

6 

16,374.39 

2,234.62 

99.84 

11.20 

10 

1 

22,365.24 

4,162.94 

232.62 

49.20 

14 

8 

16,264.64 

3,148.88 

194.39 

41.29 

10 

9 

22,239.39 

8,366.86 

265.24 

42.30 

12 

10 

1,646.62 

624.30 

42.00 

19.00 

14 

11 

9,347.27 

1,689.90 

164.69 

16.24 

8 

12 

6,362.94 

2,144.64 

196.62 

62.21 

18 

13 

976.46 

202.03 

12.13 

2.63 

14 

14 

3,274.74 

968.66 

47.31 

11.21 

12- 

15 

9,639.99 

1,244.19 

111.12 

12.16 

10 

16 

12,244.84 

2,646.29 

199.96 

35.19 

13 

n 

8,348.98 

1,294.68 

96.25 

12.12 

11 

18 

16,264.42 

3,000.99 

47.73 

10.09 

13 

19 

18,297.78 

2,346.98 

169.89 

18.94 

12 

20 

1,362.63 

423.37 

21.31 

7.96 

11 

Salesman's  total  salary  and  commissions    .     .$2,461.00 
Salesman's  total  expenses 1,992.00 


MISCELLANEOUS 

CHAPTER   XLVII 
CONSIGNMENTS  AND  COMMISSIONS 

Grain,  live  stock,  and  many  other  articles  of  produce  and  manu- 
facture are  usually  marketed  through  commission  merchants  or 
brokers. 

374.  Illustration  and  Explanation  of  Terms.  Mr.  Williams,  who 
lives  in  a  small  town  in  Minnesota,  sends  a  car  of  grain  to  Owen 
and  Bartlett,  commission  merchants  of  Chicago.  Owen  and 
Bartlett  are  engaged  to  sell  the  grain,  pay  all  charges,  deduct 
their  commission,  and  remit  the  proceeds  to  Williams. 

Williams  is  called  the  principal ;   Owen  and  Bartlett,  the  agents. 

Williams  calls  the  grain  a  shipment ;  Owen  and  Bartlett  call  it 
a  consignment.  The  statement  of  the  transaction  furnished  to 
Williams  is  called  an  account  sales.  When  a  commission  mer- 
chant is  engaged  to  buy  produce,  the  statement  of  the  transaction 
furnished  to  his  principal  is  called  an  account  purchase. 

375.  Selling  Consignments  of  Grain.  The  city  produce  ex- 
changes provide  a  ready  market  for  grain  at  all  times.  The  com- 
mission merchants  and  brokers  are  members  of  these  exchanges, 
and  act  as  the  agents  of  farmers  and  elevator  companies  in  the  sale 
of  the  grain.  The  farmer  or  elevator  owner  consigns  his  cars  of 
grain  to  his  broker,  who  sells  the  grain,  has  it  unloaded  at  the 
elevator  designated  by  the  purchaser,  receives  cash  in  payment, 
and  accounts  to  his  shipper  for  the  full  amount  received,  minus 
his  commission  and  the  charges  which  he  has  paid. 

Commission  is  the  charge  made  by  the  broker  for  handling  the 
sale.     The  following  are  Chicago  rates  : 
^  cent  per  bushel  on  corn  and  oats. 
1  cent  per  bushel  on  wheat,  rye,  and  barley. 

452 


COJSFSIGNMENTS  AND  COMMISSIONS 


453 


Inspection.  A  nominal  fee  (usually  35  cents)  is  charged  by  the 
state  grain  inspection  bureau  for  determining  the  grade  or  quality 
of  the  grain. 

Weighing.  A  fee  is  charged  by  the  board  of  trade  weighing 
bureau  for  determining  the  number  of  pounds  of  grain  in  the  car. 


SALES  BY  OWtiN  ik  BAK  1  Lt  1  I 

COMMISSION  MERCHANTS  AND  RECEIVERS 
CHICAGO 

DATE  OF  SALE 

CAR  NO 

KtND  OF  GRAIN 

LBS. 

PRICE 

TERMS 

„.„.,     1 

<:Z^,^ 

A^ 

SH-JiL/^ 

^2:^i^j!^'5^M^ 

/ii.i?s 

/  ^ 

So 

r/( 

9 

(7So 

2.0 

^V 

Pro.  No 

CHARGES 

Freight.       i-5' '/'X 

3-7 

7*^ 

Extra  Charges,         '^S(2e'^^^^c.c-tyt<l.^J:.e^ 

/ 

o  o 

Interest            /  S    days  @        tC,         <J^ 

^ 

oo 

Switching, 

Weighing. 

3o 

Inspection, 

3S 

Commission, 

6 

/3> 

^7 

^Q. 

Net  proceeds  to  your  credit, 

ao^ 

6S 

E.&O  E 

4^ 

/^ 

Soo 

GO 

CHICAGO,      C^/^f/(^              '9' 

a 

K.Cet.-un^ 

t^ 

/:^2. 

(is 

BiU  Book,  Fc 

Iw 

' 

ow 

EN  a 

BART 

_ET 

By 

b 

An  Account  Sales 


Drafts.  The  consignor  frequently  draws  a  demand  draft  on  his 
broker  in  part  payment.  The  draft  does  not  usually  exceed  80% 
of  the  estimated  value  of  the  grain.  The  shipper  deposits  the 
draft,  with  bill  of  lading  attached,  with  his  local  bank.     The  local 


454 


CONSIGNMENTS  AND  COMMISSIONS 


bank  sends  the  draft  to  its  correspondent  bank  in  the  city  where 
the  broker  is  located.  The  city  bank  presents  the  draft  to  the 
broker,  receives  payment,  and  turns  over  the  bill  of  lading.  When 
the  broker  renders  an  account  sales  of  the  grain,  he  deducts  the 
amount  of  the  draft,  plus  interest  at  the  ruling  rate  from  the  date 
the  draft  was  paid  until  the  date  on  which  he  received  the  money 
from  the  sale  of  the  grain. 

376.  Buying  Grain.  Brokers  buy  grain  as  the  agent  of  millers, 
refiners,  and  other  manufacturers  using  grain  as  a  raw  material. 
Purchases  are  made  both  for  immediate  and  for  future  delivery. 

In  the  produce  exchanges  there  is  a  quotation  on  grain  purchased 
for  immediate  delivery,  and  also  on  contracts  calling  for  the  delivery 


Purchased  By  OWEN  &  BARTLETT 

COMMISSION  MERCHANTS  AND  RECEIVERS 

CHICAGO 


For  Account  of 


^yf^^JJi'yi'^^  (yjy-t^y  ^-J^^j^C^Jto) 


9u^ 


^o  ,J^  -4-  :i  ^^f-i^<i^^@,  //  "3^ 


^ 


'-T 


^ 


/ 


c^^6^ 


JO 


/3 


An  Accouxt  Purchase 


of  grain  at  some  definite  future  date.  These  future  prices  are 
affected  by  the  prospects  of  large  or  small  crops,  by  the  demand 
for  grain  abroad,  by  the  money  market,  and  by  many  otlier  factors. 
If  the  purchase  is  made  for  immediate  delivery,  grain  is  pur- 
chased by  the  broker  for  his  principal,  at  the  market  price,  and 
delivery  is  made  as  soon  as  possible.  If  the  grain  is  purchased 
for  future  delivery,  it  is  delivered  at  the  time  specified  when  the 


CONSIGNMENTS  AND  COMMISSIONS 


455 


contract  was  made,  and  charged  at  the  price  prevailing  for  future 
orders  on  the  day  of  purchase. 

Charges  for  Buying  Grain.  The  only  charge  made  by  brokers 
for  buying  grain,  is  couimission.  The  commission  on  a  purchase 
is  the  same  as  on  a  sale. 

377.  Speculating  in  Futures.  Speculators  often  instruct  a  broker 
to  buy  grain  for  future  delivery,  hoping  that  when  the  day  of 
delivery  arrives,  the  market  price  will  have  risen  and  a  gain  may 
be  realized. 

On  the  other  hand,  a  speculator  may  instruct  his  broker  to  sell 
grain  for  future  delivery,  hoping  that  when  the  day  of  delivery 
arrives,  the  market  price  will  have  dropped.  In  such  a  case  he 
can  buy  the  grain  at  the  market  price,  and  deliver  it  to  the  pur- 
chaser at  the  contract  price,  or  the  purchaser  may  pay  him  the 
difference  between  the  market  price  and  the  contract  price. 

The  following  account  purchase  and  sale  shows  a  transaction 
in  which  a  speculator  contracted  for  the  purchase  of  September 
grain  in  July,  and  sold  it  in  September,  realizing  a  profit  of 
i  1760.00,  after  paying  his  commission. 


C^y/^^     (^.y^^^-^ 

By  OWEN  &  BARTLETT  For  Account  and  Risk  of 

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456  CONSIGNMENTS  AND  COMMISSIONS 


Table  of  Grain  Weights  per  Bushel 


Corn  56  pounds 

Wheat  60  pounds 

Oats  32  pounds 

Barley  48  pounds 


Written  Work 

1.  What  is  the  value  of  71,980  pounds  of  corn  at  62  cents  per 
bushel  ? 

2.  What  is  the  value  of  89,720  pounds  of  wheat  at  $  1.42  per 
bushel? 

3.  What  is  the  value  of  54,350  pounds  of  oats  at  52  cents  per 
bushel  ? 

4.  What  is  the  value  of  67,320  pounds  of  barley  at  81  cents 
per  bushel  ? 

5.  If  a  farmer  sells  the  elevator  company  in  his  town  514  bushels 
and  28  pounds  of  corn  at  62|  cents  per  bushel,  how  much  does  the 
farmer  receive  ? 

6.  If  an  elevator  company  buys 

514  bu.  28  lb.  of  corn  at  58|-  cents, 
312  bu.  14  lb.  of  corn  at  58J  cents, 
410  bu.  14  lb.  of  corn  at  59    cents, 

what  does  the  grain  cost  the  elevator  company  ? 

7.  If  the  elevator  company  sells  this  grain  through  a  Chicago 
broker  for  65|-  cents,  and  pays 

61  cents  per  hundred  pounds,  freight, 
J  cent  per  bushel  commission, 
25  cents  for  weighing, 
35  cents  for  inspection, 

how  much  profit  does  the  elevator  company  realize  on  the  trans- 
action ? 


CONSIGNMENTS  AND  COMMISSIONS  457 

8.  The  Sedan  Elevator  Company  shipped  you,  as  its  broker, 
1145  bushels  and  40  pounds  of  wheat,  which  you  sold  at  11.40. 
Charges  were  as  follows  : 

Commission,  1  cent  per  bushel  ; 

Freight,  8|^  cents  per  hundred  pounds ; 

Weighing,  30  cents ; 

Inspection,  35  cents. 
The  elevator  company  drew  a  draft  for  $;700,  which  you  paid 
<?leven  days  before  receiving  your  payment  for  the  grain. 
Prepare  an  account  sales  for  the  transaction. 

9.  A  milling  concern  bought  96,740  bushels,  20  pounds  of 
wheat  through  a  broker  at  f  1.40.  They  paid  freight  at  the 
rate  of  11^  cents  per  hundred  pounds,  a  commission  of  one  cent 
per  bushel,  and  switching  charges  of  $  34.  How  much  did  the 
grain  cost  them,  delivered  at  their  mills? 

10.  The  manager  of  a  breakfast  food  company  purchased  on 
April  25,  75,000  bushels  of  September  corn  at  61|-  cents.  On 
September  5,  the  price  of  September  corn  was  79|  cents.  How 
much  did  this  company  save  by  taking  advantage  of  the  lower 
price  of  corn  in  April  ?     Do  not  consider  interest. 


CHAPTER   XLVIII 
LIFE   INSURANCE 

Insurance  against  loss  due  to  sickness,  accident,  or  death 
is  called  Personal  Insurance. 

There  are  several  classes  of  Personal  Insurance  of  which  the 
following  are  the  most  common :  Accident  Insurance,  Health 
Insurance,  Liability  Insurance,  and  Life  Insurance.  Only  Life 
Insurance  will  be  considered  in  this  chapter. 

In  consideration  of  certain  payments,  called  Premiums^  a  Life 
Insurance  Company  agrees  to  pay,  at  the  death  of  the  insured,  or 
at  some  other  time  stipulated  in  the  contract,  called  the  Policy^ 
a  stated  sum  of  money  to  the  person  designated  by  the  insured. 
The  person  to  whom  payment  is  to  be  made  is  called  the  Benefici- 
ary. There  are  many  kinds  of  policies,  and  policies  of  the  same 
name  often  differ  in  certain  details. 

While  it  will  be  impossible  to  present  the  subject  of  Life 
Insurance  in  great  detail  in  this  chapter,  the  fundamental 
principles  of  the  various  types  of  policies  will  be  discussed. 

378.  Principal  Kinds  of  Life  Insurance  Policies.  The  principal 
kinds  of  policies  are  : 

a.  Ordinary  Life  policy. 
h.  Limited  Life  policy. 

c.  Endowment  policy. 

d.  Term  policy. 

These  differ  in  three  important  particulars. 

a.  The  number  of  premiums  paid  by  the  insured, 
h:  The  amount  of  each  premium. 
c.  The  time  when  payment  is  made  by  the  company. 
458 


LIFE  INSURANCE 


• 
459 


Comparison  of  Several  Kinds  of  Policies 


Kind  of  Policy 

Number  of  Years  Premiums 
ARE  Paid 

Time  when  Payment  is  Made 
BY  THE  Company 

Ordinary  Life  .     .     . 

During  life  of  insured 

[In  some  companies,  if  dividends 
are  allowed  to  accumulate  with  the 
company,  this  period  may  be  short- 

At  death  of  insured 

♦Limited  Life  — 
20-payiiient  life  .     . 
10-payment  life  .     . 

20  years 
10  years 

At  death  of  insured 
At  death  of  insured 

*Endowment  Policy  — 
20-year  endowment 

10-year  endowment 

20-payment,  30-year 
endowment     .     . 

20  years 

10  years 
20  years 

At  death  of  insured  pay- 
ment made  to  beneficiary  ; 
or  at  expiration  of  20  years 
payment  made  to  insured  if 
still  living 

At  death  of  insured  or  at 
expiration  of  10  years 

At  death  of  insured  or  at 
expiration  of  30  years 

*Term  Policy  — 
20  years    .... 

20  years 

At  death  of  insured  if  he 
dies  within  20  years.     If  he 
lives  beyond  this  term,  no 
payment  is  made 

*  The  policies  listed  under  this  heading  are  illustrative  only, 
for  other  periods  than  those  mentioned. 


Policies  are  issued 


379.  Insurance  Rates.  Insurance  rates  are  usually  quoted  at  a 
certain  price  per  $  1000  of  insurance.  The  rate  depends  upon  the 
age  of  the  insured  when  he  "  takes  out  the  policy,"  and  upon  the 
kind  of  policy.     The  premiums  are  payable  in  advance. 

The  desirability  of  insuring  at  as  early  an  age  as  practicable,  is 
shown  by  a  study  of  the  comparative  premiums  at  different  ages. 

The  following  table  shows  the  premium  rates  per  thousand  on 
various  kinds  of  policies  for  various  ages. 


460 


LIFE  INSURANCE 


Annual  Premium  on  Different  Kinds  of  Insurance 
PER  $1000.00 


Age 

15 
20 
25 
30 
35 
40 
45 
50 
55 
60 
65 


Ordinary 
Life 

17.40 

20-Pay. 
Life 

127.34 

10-Pay. 
Life 

$  44.62 

10-Yeab 
Endowment 

$100.60 

20-Yeab 
Endowment 

147.79 

19.21 

29.39 

47.85 

101.57 

48.48 

21.49 

31.83 

51.67 

102.73 

49.33 

24.38 

34.76 

56.18 

104.14 

50.43 

28.11 

38.34 

61.53 

105.87 

51.91 

33.01 

42.79 

67.90 

108.07 

54.06 

39.55 

48.52 

75.57 

111.03 

57.34 

48.48 

56.17 

84.99 

115.28 

62.55 

60.72 

66.69 

96.66 

121.48 

70.81 

77.69 

81.60 

111.47 

130.76 

83.82 

101.48 

131.13 

145.08 

Written  Work 

From  the  preceding  table  find  the  annual  premium  required 
for : 

1.  An  ordinary  life  policy  for  $4000,  taken  by  a  man  20  years 
of  age. 

2.  A  ten-payment  life  policy  for  $3000,  taken  by  a  man  25 
years  of  age. 

3.  A  ten-year  endowment  policy  for  $5000,  taken  by  a  man  35 
years  of  age. 

4.  A  twenty-year  endowment  policy  for  $5000,  taken  by  a  man 
25  years  of  age. 

5.  A  man  25  years  of  age  took  out  a  twenty-j^ear  endowment 
policy  for  $5000,  and  died  after  making  eight  payments.  How 
much  less  would  the  combined  premiums  have  been  on  an  ordinary 
life  policy? 

6.  A  man  on  his  30th  birthday  took  out  a  twenty-payment  life 
policy  for  $3000,  and  5  years  later  he  took  out  an  ordinary  life 
policy  for  $5000.  He  died  after  making  fifteen  payments  on  his 
first  policy.  By  how  much  did  the  insurance  received  by  his  bene- 
ficiary exceed  the  premiums  paid  (not  considering  accumulations)? 


LIFE  INSURANCE 


461 


380.  Dividends.  Policies  written  on  the  "  participating  plan  " 
provide  that  a  portion  of  the  annual  profits  of  the  company  shall 
be  shared  by  the  holders  of  the  policies.  These  annual  payments 
of  a  share  of  the  profits  are  called  "  dividends."  Since  the  profits 
of  the  company  vary  from  year  to  year,  no  specific  amount  of 
dividend  is  guaranteed  to  the  policyholder.  Policyholders  usually 
receive  no  dividend  the  first  year.  Dividends  may,  at  the  option 
of  the  insured,  be 

a.    Paid  to  him  in  cash ; 

h.    Applied  to  the  payment  of  his  premium  ; 

c.  Left  with  the  company  and  allowed  to  accumulate  at  com- 
pound interest ; 

d.  Left  with  the  company  to  increase  the  amount  of  insurance 
carried  ; 

e.  Left  with  the  company  in  order  to  decrease  the  number  of 
payments  of  premiums. 

The  following  table  shows  the  effect  of  the  dividends  in  reduc- 
ing the  annual  premiums. 

Annual  Cash  Dividends  and  Net  Cost  of  Insurance  on  Policies 
OF  $1000— Age  35 


Okdinary  Life  Policy 

Issued  in  1908. 
Annual  Premium,  $27.30 

20-Premium  Life  Policy 

Issued  in  1908. 
Annual  Premium,  $36.00 

20- Year  Endowment 

Policy 

Issued  in  1908. 

Annual  Premium,  $50.80 

Year 
Ending 

Dividend  at 
End  of  Year 

Cost  for 
Each  Year 

Dividend  at 
End  of  Year 

Cost  for 
Each  Year 

Dividend  at 
End  of  Year 

Cost  for 
Each  Year 

1908 

1 

$3  00 

$24  30 

$  3  30 

$32  70 

$3  80 

$47  00 

1909 

2 

3  10 

24  20 

3  45 

32  55 

4  05 

46  75 

1910 

3 

3  20 

24  10 

3  60 

32  40 

4  35 

46  45 

1911 

4 

4  10 

23  20 

4  40 

3160 

4  95 

45  85 

1912 

5 

4  25 

23  05 

4  60 

31  40 

5  25 

45  55 

1913 

6 

4  70 

22  60 

5  30' 

30  70 

6  60 

44  20 

1914 

7 

5  25 

22  05 

6  05 

29  95 

7  70 

43  10 

1915 

8 

5  80 

2150 

6  75 

29  25 

8  65 

42  15 

1916 

9 

6  30 

2100 

7  30 

28  70 

9  30 

4150 

1917 

10 

6  50 

20  80 

7  55 

28  45 

9  65 

41  15 

462  LIFE  INSURANCE 

381.  Lapses.  If  the  annual  premium  is  not  paid  when  due,  the 
policy  lapses.  However,  most  companies  allow  one  month's 
grace,  during  which  time  the  overdue  premium  may  be  paid  with 
interest.  If  death  occurs  during  this  period  of  grace,  the  amount 
of  the  overdue  premium  and  the  accrued  interest  are  deducted  in 
making  settlement  with  the  beneficiary. 

If  the  premium  remains  unpaid  after  the  expiration  of  the 
period  of  grace,  the  policy  may  be  reinstated,  but  the  policy- 
holder must  furnish  satisfactory  evidence  of  health  and  pay  all 
back  premiums  with  accrued  interest. 

382.  Cash  Surrender,  Loan,  and  Paid-up  Insurance.  After  a 
policy  has  been  in  force  for  a  certain  number  of  years  (usually 
two  or  three),  many  companies  offer  the  insured  the  following 
privileges : 

a.    Borrowing  money  from  the  company ; 

h.    Surrendering  the  policy  for  a  cash  payment ; 

c.  Receiving  a  "  paid-up  "  policy  which  gives  a  fixed  amount  of 
insurance  during  the  remainder  of  life  without  further  payment 
of  premiums. 

d.  Being  insured  for  the  face  of  the  policy  for  a  fixed  number 
of  years  and  months. 

For  example,  after  an  ordinary  life  policy  for  f  1000.00,  taken 
at  the  age  of  35,  in  a  certain  company,  has  been  in  force  8  years, 
the  insured  can  — 

a.  Borrow  $108.00  from  the  company  on  the  security  of  the 
policy. 

5.    Surrender  the  policy  and  receive  $108.00  in  cash. 

c  Cease  the  payment  of  premiums  and  be  insured  for  the 
remainder  of  his  life  for  $223.00. 

d.  Cease  the  payment  of  premiums  and  be  insured  for  $1000.00 
for  10  years  and  9  months. 

383.  Modes  of  Settlement.  Upon  proof  of  the  death  of  the 
insured  (or,  in  case  of  an  endowment  policy,  at  the  expiration  of 
the  endowment  period),  the  policy  becomes  payable  by  the  com- 
pany. Settlement  may  be  made  in  a  variety  of  ways,  the  most 
common  of  which  are  : 


LIFE  INSURANCE  463 

a.    Payment  of  cash  to  the  beneficiary ; 

h.  Annual  payment  of  interest  during  the  life  of  the  benefici- 
ary, and  payment  of  the  face  of  the  policy  at  the  death  of  the 
beneficiary; 

c.  Payment  of  equal  annual  installments  for  the  number  of 
years  specified  to  the  beneficiary  ; 

d.  Payment  of  equal  annual  installments  for  a  period  of  twenty 
years,  and  for  as  many  years  thereafter  as  the  beneficiary  shall 
live.  The  amount  of  each  annual  payment  depends  upon  the  age 
of  the  beneficiary  at  the  death  of  the  insured. 

Oral  Work 

1.  Explain  the  reason  for  the  difference  in  the  premiums  of 
the  different  kinds  of  policies. 

2.  Why  is  it  often  wise  to  take  insurance  at  an  early  age  ? 

3.  What  is  participating  insurance  ? 

Written  Work 

Refer  to  the  table  of  annual  premiums  on  different  kinds  of 
insurance  and  find  the  annual  premium  on  the  following : 

1.  %  2000,  ordinary  life  policy,  taken  at  the  age  of  35. 

2.  $5000,  20-year  endowment  policy,  taken  at  the  age  of  35. 
^     3.    $3000,  10-payment  life  policy,  taken  at  the  age  of  35. 

4.  $6000,  20-payment  life  policy,  taken  at  the  age  of  35. 

5.  $10,000,  10-year  endowment  policy,  taken  at  the  age  of  35. 

6.  On  his  25th  birthday  Mr.  Anderson  took  out  a  20-payment 
life  policy  for  $3000;  on  his  30th  birthday  he  took  out  a  20-year 
endowment  policy  for  $5000 ;  on  his  35th  birthday  he  took  out 
an  ordinary  life  policy  for  $7000.  He  died  at  the  age  of  38 
years  7  months.  How  much  more  did  his  beneficiary  receive 
(dividends  excepted)  than  he  paid  the  company  ?  (Use  the  table 
on  page  460.) 


CHAPTER   XLIX 
FARM  RECORDS 

384.  The  Cash  Book.  One  of  the  most  important  records  for 
a  farmer  is  tlie  cash  book,  in  which  he  can  tabulate  the  various 
sources  of  his  income  and  the  amounts  of  his  various  expenditures. 

The  following  are  three  of  the  forms  which  may  be  used  for 

this  purpose : 

A 

Receipts       Expbnditttres 


1917 

Oct. 

1 

Balance 

123 

75 

1 

15  bu.  apples  @  .70 

10 

50 

1 

12  doz.  eggs    @  .30 

3 

60 

3 

Groceries 

5 

95 

5 

Lumber 

B 

26 

25 

Eeoeipts 


Expenditures 


1917 

Oct. 


Balance 

15  bu.  apples  @  .70 

12  doz.  eggs  @  .30 


123 


75 


1915 

Oct. 


Groceries 
Lumber 


C 

Eeceipts 


1917 

Item 

Dairy 

Poultry 

Crops 

General 

May 

1 
2 
3 

2  cows  to  Owen 
10  doz.  eggs  @  .28 
4  T.  hay 

125 

00 

2 

80 

60 

00 

464 


FARM  RECORDS 


465 


EXPENDITUBKS 


1915 

Item 

Dairy 

POULTKT 

Cbops 

HotrSEHOLD 

General 

May 

1 

500  #  bran 

8 

00 

2 

10  bu.  seed  oats 

10 

00 

3 

Groceries 

3 

60 

4 

Oyster  shell 

1 

50 

5 

Cement 

8 

00 

lures  " 
Marcli 


Written  Work 

Rule  a  form  for  a  cash  book  similar  to  the  last  illustration. 
Include  an  extra  column  in  both  "  Receipts "  and  "  Expendi- 
labeled  "  Stock  "  and  enter  the  following  facts  : 

1,  Balance,  i  280. 00. 

1,  Sold  for  cash  1  carload  hogs,  11080.00. 

1,  Bought  2  cows,  $45.00  and  158.00. 

2,  Bought  1  set  double  work  harness,  $21.00. 

3,  Bought  1  work  horse,  $160.00. 

4,  Sold  30  doz.  eggs  at  25  cents. 

5,  Sold  8  T.  timothy  hay  at  $14.00  per  ton. 

6,  Sold  1  wagon  load  oats  to  elevator,  95  bu.,  at  46  cents. 
6,  Bought  groceries,  $7.95. 

8,  Sold  one  second-hand  riding  plow,  $15.00. 

9,  Bought  20  sacks  cement  at  $.50. 

10,  Bought  90  bu.  seed  oats  at  48  cents. 

11,  Bought  500  #  middling  for  hogs  at  $30.00  per  ton. 

12,  Bought  2  riding  plows  at  $55.00  each. 

15,  Received  milk  check  for  30  da.,  $26.47. 

16,  Bought  groceries,  $6.83. 

17,  Bought  wheat  screening  for  chickens,  $2.50. 
20,  Sold  2  steer  calves  at  $9.00  and  $12.00. 
22,  Sold  18  young  roosters,  57  #  at  14^  per  pound. 
24,  Rented  a  three-horse  team  to  a  neighbor  for  2J  da.  at 

$3.75  per  day. 
26,  Bought  10  T.  rock  phosphate  at  $3.00  per  ton. 


466  FARM  RECORDS 

28,  Sold  28  doz.  eggs  at  27  cents. 

28,  Bought  1  pair  shoes,  12.85 ;  suit  of  clothes,  $11.00. 
Find  the  total  receipts  and  expenditures  for  each  column,  and 
the  balance  at  the  end  of  the  month. 

385.  Farm  Profits.  The  annual  increase  or  decrease  of  the 
farmer's  wealth  may  be  determined  by  taking  an  inventory  each 
year,  and  comparing  it  with  the  inventory  of  the  preceding  year. 
The  inventory  should  be  classified  to  show  the  capital  invested 
in  land,  building,  live  stock,  machinery,  and  other  property.  An 
inventory,  taken  from  Farmers'  Bulletin  511,  U.  S.  Department 
of  Agriculture,  is  reproduced  on  pages  467  and  468. 

386.  What  is  Farm  Profit  ?  The  annual  increase  shown  by  the 
two  inventories  is  not  the  farmer's  net  gain  for  the  year.  The  real 
annual  profit  is  found  by  the  following  method : 

Increase  shown  by  inventories,  plus  living  supplied  by  farm  to 
family,  plus  interest  paid  on  indebtedness,  minus  interest  on 
capital  invested,  minus  wages  of  farmer  and  family,  equals  actual 
net  profit. 

Example.  Let  us  suppose  the  inventories  show  an  increase  for 
the  year  of  f  2000.  The  farm  has  also  supplied  a  residence  and 
provisions  for  the  farmer's  family.  .  If  the  house  rent  is  estimated 
at  $  120  and  the  supplies  are  valued  at  $  900,  the  total,  $  1020, 
should  be  credited  to  the  farm.  Adding  $80  interest  paid  on  the 
farm  mortgage,  we  have  the  following : 

$2000     Increase  of  inventory 
1020     Household  expenses 
80     Interest  paid 
$3100     Produced  by  farm 

The  farmer  has  $10,000  invested  in  the  farm.  If  this  money 
were  loaned  at  5  %  interest,  it  would  produce  $500  interest  annu- 
ally.    $500  interest  must  therefore  be  subtracted. 

If  the  farmer  had  worked  for  some  one  else,  he  might  have  earned 
wages  of,  say,  $  700.  This  amount  must  also  be  subtracted  in  order 
to  determine  real  profit. 

Thus,  we  have 

$3100  -  $500  (interest)^  $700  (wages)  =  $1900,  profit. 


FARM  RECORDS 

Sample  farm  inventory :     Farm  of_ 


467 


Pkopektt 

April  1,  1916 

April  1,  1917 

No. 

Kate 

Valuation 

No. 

Rate 

Valuation 

BEAL  ESTATE 

Farm  of  180  acres  (155  tillable), 
including:  buildings  (dwelling 
$1,600,    barns    $1,800,    other 
buildings    $600),  fences,   and 
other  improvements 

$13,500.00 

$13,500.00 

.uIVE   STOCK 

Dairy  cattle : 

Cows,  dry  and  in  milk 

Bull 

24 

1 
6 
4 

$50.00 

14.00 
28.00 

$  1,200.00 

50.00 

84.00 

112.00 

1,446.00 
76.00 

1,100.00 
107.00 

26 
1 
8 
6 

$50.00 

15.00 
20.00 

$  1,300.00 
45.00 
120.00 
120.00 

Calves 

Two-year-olds 

Total  value  of  dairy  cattle 

1,585.00 

Hogs : 

Brood  sows 

Pigs 

2 

8 

22.00 
4.00 

44.00 
.32.00 

2 
6 

21.00 
8.00 

42.00 
IS.OO 

Total  value  of  hogs 

60.00 

Horses : 

Horse,  Jim,  7  years  old 

Team,  Nell  and  Bess,  5  and 

6  years  old 

Team,  Jack  and  Prince,  6 

and  7  years  old 

Colt,  1  year  old 

1 

1 

1 
1 

200.00 

425.00 

400.00 
75.00 

1 

1 
1 

180.00 

425.00 

400.00 
145.00 

Total  value  of  horses 

1,150.00 

Poultry : 

Hens 

Roosters 

Turkeys 

160 
5 
2 

.60 
1.00 
3.00 

96.00 
5.00 
6.00 

125 
4 
3 

.60 
1.00 
8.00 

75.00 
4.00 
9.00 

Total  value  of  poultry 

88.00 

Total  value  of  live  stock.. 

2,729.00 

2,888.00 

MACHINEBY   AND   TOOLS 

Grain  binder 

1 
2 
2 

1 
1 

45.00 
28.00 

90.00 
90.00 
56.00 
85.00 
20.00 

475.00 

1 
2 
2 

1 
1 

41.00 
25.00 

82.00 
82.00 
50.00 
30.00 
19.00 

Mower 

Hay  rake 

(List  all  items   of  farm  ma- 
chines,    wagons,     harness, 
and  small  tools.) 

Total  investment  in  ma- 
chinery and  tools  (not 
all  listed  here) 

461.00 

468 


FARM  RECORDS 


Sample  farm  inventory :    Farm  of  - 


— (Continued) 


April  1,  1916 

April  1,  1917 

No. 

Rate 

Valuation 

No. 

Rate 

Valuation 

FEED   AND   SUPPLIES 

Farm  products : 

Corn bushels. . 

Oats do.... 

Potatoes do 

Hay,  timothy tons  . . 

Hay,  mixed do 

Silage do.... 

Bran do 

80 

■200 

40 

10 

5 
40 

Oi 

1 
30 
45 

3 

4 
20 

.60 

.42 

.75 

16.00 

12.00 

4.00 

.80 
.80 
2.00 
.50 
.10 

48.00 

84.00 

30.00 

160.00 

60.00 

160.00 

15.00 

31.00 

24.00 

86.00 

6.00 

2.00 

2.00 

658.00 

125 
90 
80 
20 
4 
40 

.60 

.50 

.60 

16.00 

12.00 

4.00 

75.00 
45.00 
48.00 
•      300.00 
48.00 
160.00 

Mixed  feed do.... 

Seed  oats      bushels. . 

35 
50 
3 

30.00 

.80 

1.00 

2.00 

75.00 

28.00 

50.00 

6.00 

Seed  potatoes do.... 

Seed  corn do.... 

Cement sacks. . 

Twine pounds- . 

10 

.10 

1.00 

Total  value   of  feed  and 
supplies 

&36,00 

BILLS   BECEIVABLE 

J.  A.  Brown,  hay tons. . 

R.  S.  Jones,  potatoes,  .bushels. . 

2 

40 

13.00 
.50 

26.00 
20.00 

46.00 

210.00 
1,938.00 

Total 

CASH 

On  hand 

90.00 
580.00 

670.00 

In  bank 

Total 

2.148.00 

BILLS   PAYABLE 

Farm  mortgage 



2,000.00 

1,500.00 

13,500.00 
2,729.00 
475.00 
658.00 
46.00 
670.00 

13,500.00 

2,883.00 

461.00 

886.00 

SUMMARY 

Eeal  estate 

18,078.00 
2.000.00 

Live  stock 

Machinery  and  tools 

Feed  and  supplies 

Bills  receivable 

Cash  on  hand  and  in  bank 

2.148.00 

Total  investment 

19,828.00 
1.500.00 

Bills  payable 

Net  worth 

16,078.00 

18,328.00 

Increase  in  inventory  $2,250. 

FARM  RECORDS 


469 


Real  profit  may  be  determined  by  the  preparation  of  a  statement 
similar  to  the  following: 


Item 

March  1,  1917 

March  1,  1918 

Resources 

Real  estate 

$15,000 

$15,000 

Live  stock 

3,160 

3,590 

Machinery  and  tools 

530 

575 

Feed  and  supplies 

860 

735 

Cash 

140 

275 

Bills  receivable 

50 

Accounts  receivable 

93 

126 

Total  resources 

19,783 

20,351 

Liabilities 

Accounts  payable 

135 

60 

215 

20 

Mortgage 

1,000 

1,000 

Total  liabilities 

1,135 

60 

1,215 

20 

Present  worth 

18,647 

40 

19,135 

80 

Increase  in  net  worth 

488 

40 

Add 

Interest  paid  on  mortgage  5%  on  $1000 

50 

Personal  and  household  expenses  paid  in  cash 

750 

Supplies  furnished  by  farm  for  household 

363 

Rent  of  farmhouse 

120 

Gross  farm  gain 

1,771 

40 

Deduct 

Interest  on  net  investment  at  5  % 

932 

37 

Labor  of  owner  and  family  (estimated) 

600 

1,532 

Total  deduction 

37 

True  net  gain 

239 

03 

Written  Work 

From  the  following  facts  prepare  a  statement  similar  to  the  pre- 
ceding illustration. 

Condition  of  farmer's  affairs  on  March  1,  1917. 

He  owns  a  farm  of  160  acres,  worth  f  225  per  acre,  on  which  he 
has  given  a  mortgage  of  $6000,  bearing  5  %  interest.  Cash  on 
hand  and  in  bank,  $  345.85.     His  live  stock  is  worth  f  5280 ;   his 


470  FARM  RECORDS 

poultry,  f  286;  his  machinery,  $1250;  unsold  crops,  $900.  He 
has  just  sold  a  car  of  hogs  to  a  local  stock  buyer,  who  owes  him 
$975  for  them.  He  also  has  on  hand  fertilizer,  lumber,  and 
other  supplies  worth  $387.50.  He  owes  sundry  accounts,  amount- 
ing to  $236.25. 

During  the  year  betw^een  March  1,  1917,  and  March  1,  1918,  he 
paid  the  interest  on  his  mortgage,  and  also  paid  $1000  on  the 
principal  of  the  mortgage.  He  paid  by  cash  and  by  butter,  eggs, 
and  other  produce,  for  household  expenses,  $596.50.  He  estimated 
the  rent  of  his  house  at  $15  per  month;  the  produce  of  the  farm 
consumed  by  the  family,  $645;  and  his  wages,  $600.  He  paid 
taxes  and  insurance,  $275.  Compute  interest  on  net  investment 
at  the  beginning  of  the  year  at  5  %. 

On  March  1,  1915,  he  had,  cash  $167.20;  live  stock,  $6140; 
poultry,  $270;  machinery,  same  as  previous  year,  less  10  %  depreci- 
ation, plus  $165  worth  of  new  machinery;  crops  on  hand,  $650  ; 
miscellaneous  supplies,  $295.  He  owes  personal  accounts  amount- 
ing to  $193.70  and  the  unpaid  balance  of  the  mortgage. 

387.  Finding  the  Profits  by  Crops.  In  order  to  determine  the 
profit  from  any  particular  crop,  the  farmer  must  know : 

a.  The  value  of  the  crop  produced ; 

b.  The  cost  of  producing  the  crop,  including  seed,  fertilizer, 
labor,  and  a  share  of  the  taxes,  interest,  and  general  expenses. 

388.  Determining  the  Expenses.  The  cost  of  seed  and  fertilizer 
may  be  determined  with  comparative  ease,  because  measurable 
quantities  are  put  on  each  field. 

Taxes,  interest,  and  general  expenses  are  prorated  among  the  dif- 
ferent crops  in  the  ratio  of  the  land  occupied. 

Example.  A  farmer  who  has  40  acres  of  hay,  60  acres  of 
corn,  and  30  acres  of  oats  under  cultivation,  finds  that  his  total 
interest,  taxes,  and  expenses  are  $1200.  How  should  this  be 
prorated  ? 

Solution.    $1200-4-130  =  ^9.23  Charge  per  acre. 

40  X  $  9.23  =  $  369.20  Share  for  hay  crop. 

60  X  $  9.23  =  $  553.80  Share  for  corn  crop. 

30  X  $9.23  =  $276.90  Share  for  oat  crop. 


FARM  RECORDS 


471 


Labor  of  men  and  horses  must  be  determined  by  records  of  the 
actual  labor  spent  on  each  crop. 

•Accurate  labor  records  may  be  obtained  by  a  daily  time  mem- 
orandum similar  to  the  following  illustration  : 

Regular  Worker  s  Daily  Time  Sheet 

,m/yKruituii  iuiiii  ^^^    — ^ j^  i 


V«rmA. 


(/.  B.  Department  of  Agriculture 
in  cooperation  -with 


KIND  OF  WORK. 
.Inclwlo  liii(>Ieiii(.'iits  uv.sl,  iiumiUt  uf  totuU,  etc< 


00 

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TOTAL  HOURS 


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REPORT  O.  K. 


472 


FARM  RECORDS 


From  the  foregoing  record  a  summary  may  be  made  on  a  blanl^ 
form  like  the  following  illustration.  At  the  end  of  the  montl: 
the  column  totals  will  show  the  number  of  man  hours  and  horse 
hours  of  labor  expended  on  each  of  the  farm's  crops  or  othe^ 
industries. 


MONTH     Oiy,5i4**< 

MONTHLY   ' 

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FARM  RECORDS 


473 


Cost  of  a  horse  hour  is  determined  in  a  similar  way. 
Total  value  of  2  horses,  $600.00 
Int.  on  $  600.00  at  5  %,  $  30.00 

Feed  and  expense,  550.00 

Total  cost  per  year,         1 580.00 
Total  number  of  horse  labor  hours,  6500. 

$  580.00  -^  6500  =  8.9  cents,  labor  cost  per  horse  hour. 

After  the  labor  cost  records  have  been  made,  the  profit  or  loss 
from  the  crop  may  be  determined  by  the  preparation  of  a  table 
similar  to  the  following  : 

Account  with  a  Crop  of  Corn  in  Field  B  (36.48  Acres)  on  an  Iowa 

Farm,  ]910i 


Date 

Total 

Per  Acre 

Per 

bushel 

Items  op  Statement 

Man 
hours* 

Horse 
hours  * 

Cost 

Man 

hours  * 

Horse 
hours  2 

Cost 

Plowing,  fall  of  1909  (14- 
inch  gang)      .     ,     .     . 

Disking 

Harrowing 

Planting  (with  planter) 

Harrowing  (after  plant- 
ing)   

Cultivating  (tirst  time)  . 

Cultivating    (second 
time) 

Cultivating  (third  time) 

Cultivating  (fourth  time) 

Picking  seed  corn  .     .     . 

Husking  (from  standing 
stalks) 

Mar.  25  to  Apr.  2 
Apr.  7  to  29 
Apr.  29  to  May  4 
Apr.  30  to  May  5 

Mav  10  to  14 
May  27  to  30 

June  3  to  6 
June  14  to  18 
June  23  to  July  5 
Sept.  27  to  Oct.  7 

Nov.  2  to  22 

90i 
30§ 

58 

545 
51-1 
57 
59 

305J 

342 
361 

51 

61 

72i 
116 

109 
103 
114 

$46.48 

49.28 

8.56 

10.25 

11.86 
19.49 

18.31 

17.31 

19.15 

7.44 

102.65 

2.34 

2.47 

.70 

.84 

.92 
1.59 

1.49 
1.41 
1.56 
1.62 

8.38 

9.38 

9.89 
1.40 
1.67 

1.99 
3.18 

2.99 

2.82 
3.12 

$1,279 

1.351 

.235 

.281 

.325 
.534 

.502 
.474 
.625 
.204 

2.814 

611 

16.75 

Total  labor  cost  ,     . 
Manure  charge    .     . 
Seed,  5i  bushels,  at 

$5 

General  expense .     . 
Equipment      .     .     . 

Taxes     

Interest  (rent)     .    . 

851 

1,940J 

310.98 
124.91 

27.50 
18.24 
23.27 
25.53 
255.35 

23.32 

53.19 

8.524 
3.424 

.754 
.500 
.638 
.700 
7.000 



Total  cost     .    . 

78.5.78 

91.54 

Summary : 

Income  3     .... 
Cost 

1,127.36 

785.78 

30.90 
21.54 

$0,512 
.357 

Profit 

331.58 

9.36 

.155 

1  Previous  crop  :    Timothy  for  seed,  1909. 

2  Rates  per  hour :    Man  hours,  12.6  cents  ;  horse  hours.  10.5  cents, 

»  Yield  :  2200  bushels  of  grain,  at  50  cents  (average,  60.3  bushels  per  acre),  $  1100  ;   stalks,  $  27.86 ; 
total,  $  1127.36. 


474 


FARM  RECORDS 


The  labor  records  show  the  number  of  horse  hours  and  man 
hours  spent  on  each  crop*  After  determining  the  hourly  rate,  it 
is  necessary  to  multiply  as  follows : 

The  number  of  man  hours  by  the  rate  per  man  hour ;  the  num- 
ber of  horse  hours  by  the  rate  per  horse  hour ;  to  determine  the 
total  labor  cost  of  each. 

The  costs  and  returns  of  each  crop  may  then  be  summarized, 
and  the  gain  computed,  as  illustrated  in  the  following  table : 

Corn  Crop  on  South  40 


Item 

40  Acres 

Pee  Acre 

Seed 

$    24.00 

70.00 

28.30 

450.00 

40.00 

109.01 

228.60 

.60 

Fertilizer 

1.75 

Taxes 

.7075 

Interest     

11.25 

Expense 

1.00 

Man  labor,  991  hours  at  11  cents      .     . 
Horse  labor,  2286  hours  at  10  cents 



2.725 
5.715 

Total  cost 

949.91 

23.7475 

Yield,  2552  bu.  corn  at  1.48     .... 
Stalks,  75^  per  acre 

.     $1224.96 
30.00 

1254.96 
949.91 

a 

Total  returns 

31.374 

23.7475 

Gain 

305.05 

7.6265 

The  illustrations  in  this  section  are  reprinted  by  permission  from  Farmers' 
Bulletin  511,  U.  S.  Department  of  Agriculture. 


Written  Work 

1.  Find  the  labor  cost  to  be  charged  against  the  corn  crop,  in 
the  production  of  which  136  man  hours  and  312  horse  hours  of  labor 
were  expended.  The  total  number  of  hours  of  man  labor  for  the 
year  was  4825,  and  the  annual  cost  was  $868.50;  total  number 
of  hours  of  horse  labor,  4312 ;  total  cost  of  horse  labor  for  the 
year,  1388.08. 

2.  Use  the  following  facts  to  prepare  a  table  similar  to  the 
model  above  : 


FARM  RECORDS  475 

Corn  Crop  on  20  Acres 

Yield :  10  bushels  of  seed  corn  worth  |3.50  per  bushel. 

Corn  crop  harvested,  67  bushels  per  acre,  worth  54  cents 

per  bushel. 
Stalks  were  estimated  at  a  value  of  60  cents  per  acre. 

Costs :  3^  bushels  of  seed  at  i4.50  per  bushel. 

Fertilizer,  $  38.00. 

Taxes :  The  farm  was  worth  $  175.00  per  acre,  and  was 
taxed  on  ^  the  real  value  at  a  rate  of  $1.65.  The 
farm  contained  160  acres,  and  the  taxes  were  prorated 
among  the  various  fields  in  proportion  to  their  acreage. 

Interest :  4  %  on  the  value  of  the  land. 

Expense:  #31.25. 

Labor :  560  man  hours  at  19  cents. 
1348  horse  hours  at  9  cents. 


APPENDIX 


DENOMINATE   NUMBERS 

SURVEYORS'  LONG  MEASURE 

7.92  inches  =  1  link  (Ik.) 

25  links  =  1  rod 

4  rods,  or  100  links  =  1  chain  (ch.) 
80  chains  =  1  mile 


SURVEYORS'   SQUARE  MEASURE 

625  square  links     =  1  square  rod 
10  square  rods      =  1  square  chain 
16  square  chains  =  1  acre 
640  acres  =  1  square  mile 

36  square  miles    =  1  township 
The  following  units  of  measure  are  used  by  sailors : 

6  feet  =  1  fathom     (Used  for  measuring  depths  3,1 

sea.) 
120  fathoms  =  1  cable  length  (Used  for  measuring  depths 

at  sea.) 
About  1.15  statute  miles  =  1  knot,  or  1  nautical  mile,  or  6080.27  ft. 


CIRCULAR  OR  ANGULAR  MEASURE 

60  seconds  (60")  =  1  minute  (') 
60  minutes  =  1  degree  (1°) 

90  degrees  =  1  right  angle 

360  degrees  =  1  circumference 


TROY  WEIGHT 

24  grains  (gr.)      =  1  pennyweight  (pwt.  ordwt.) 
20  pennyweights  =  1  ounce  (oz.) 
12  ounces  =  1  pound  (lb.) 

477 


478  APPENDIX 


APOTHECARIES'   WEIGHT 

20  grains  (gr.)     =  1  scruple  (sc.  or  3) 
3  scruples  =  1  dram  (dr.  or  3  ) 

8  drams  =  1  ounce  (oz.  or  3  ) 

12  ounces  =  1  pound  (lb.) 

Apothecaries'  weight  is  used  by  physicians  and  druggists.     Troy  weight  is 
used  in  the  measurement  of  precious  metals. 

COMPARISON  OF  TROY  AND  AVOIRDUPOIS  WEIGHTS 

1  pound  Troy  •    =  5760  grains 

1  pound  avoirdupois  =  7000  grains 
1  ounce  Troy  =  437^  grains 

1  ounce  avoirdupois  =    480  grains 

The  term  carat  has  two  meanings : 

In  weighing  precious  stones,  a  carat  usually  means  3.2  Troy  grains. 
In  expressing  the  purity  of  gold,  24  carats  means  pure  gold ;  18  carats  means 
Jf  pure  gold,  and  ^^  alloy. 

PAPER  MEASURE 

24  sheets  =  1  quire  (qr.) 
20  quires  =  1  ream  (rm.) 
Although  a  ream  contains  480  sheets,  500  sheets  are  usually  sold  as  a  ream. 

STANDARD  UNITS  OF  WEIGHT 

1  barrel  flour  weighs  196  pounds 

1  barrel  salt  weighs  280  pounds 

1  barrel  pork  or  beef  weighs  200  pounds 
1  keg  of  nails  weighs  100  pounds 

STANDARD  BUSHELS  IN  MANY  STATES 

1  bushel  shelled  corn  weighs  56  pounds 
1  bushel  ear  corn  weighs  70  pounds 
1  bushel  wheat  weighs  60  pounds 

1  bushel  barley  weighs  48  pounds 

1  bushel  rye  weighs  56  pounds 

1  bushel  oats  weighs  32  pounds 

TABLE  OF   ABBREVIATIONS   USED  IN   BUSINESS 
(The  singular  form  is  commonly  used  for  both  the  singular  and  plural.) 

A.     .     .     .  acre  ans.  .  .  .  answer 

acct.ora/c.  account  Apr.  .  .  April 

agt.       .     .  agent  Aug.  .  .  August 

amt.      .     .  amount  av.    .  .  .  average 


APPENDIX 

479 

TABLE  OF  ABBREVIATIONS  USED  IN  BUSINESS  —  (con^nz^d) 

.  bag;  bags 

ea.    . 

.     .  each 

.  balance 

e.g. 

.     .  for  example 

)rl.  barrel 

e.o.e. 

.     .  errors  and  omissions  ex- 

. bundle 

cepted 

.  basket 

etc.. 

.     .  and  so  forth 

.  bale 

ex.    . 

.     .  example;  express 

.  bill  of  lading 

exch. 

.     .  exchange 

.  bought 

exp. 

.     .  expense 

.  bushel 

f.      . 

.     .  franc 

.  box 

far.  . 

.     .  farthing 

.  one  hundred 

Feb. 

.     .  February 

.  cord  ;  card 

fir.    . 

.     .  firkins 

.  centigram 

f.o.b. 

.     .  free  on  board 

.  chain;  chest 

frt.   . 

.     .  freight 

.  charge 

ft.     . 

.     .  foot 

.  carriage  and  insurance  free 

gal.  . 

.     .  gallon 

.  check 

gi-    • 

.     .  gill 

.  centimeter 

gr.    • 

.     .  grain 

.  commercial 

gro.  . 

.     .  gross 

.  care  of 

^'^'g^ 

'0.      .  great  gross 

.  company ;  county 

guar. 

.     .  guaranty;  guarantee 

.  collect  on  delivery 

hf.    . 

.     .  half 

.  collection 

hf.  cl 

it.      .  half  chest 

.  commission 

hhd. 

.     .  hogshead 

.  consignment 

hr. 

.     .  hour 

.  creditor;  credit;  crate 

i.e. 

.     .  that  is 

.  case 

in.  '. 

.     .  inch;  inches 

.  cask 

ins. 

.     .  insurance 

.  cent;  centime 

inst. 

.     .  instant;  the  present  month 

.  cubic  foot 

int.  . 

.     .  interest 

.  cubic  inch 

I.;h 

IV.      .  invoice 

.  cubic  yard 

inv't 

.     .  inventory 

.  hundredweight 

Jan. 

.     .  January 

.  pence 

kg. 

.    .keg 

•  day 

km. 

.     .  kilometer 

.  December 

1. 

.     .  link 

.  department 

lb. 

.     .  pound 

.  draft 

l.p. 

.     .  list  price 

.  discount 

ltd. 

.     .  limited 

.  ditto  (the  same) 

M 

.     .     .  one  thousand 

.  dozen;  dozens 

m. 

.     .     .  mill;  meter 

.  debit;  debtor;  doctor 

Mar. 

.     .  March 

.  East 

mdse 

.    .     .  merchandise 

480 

APPENDIX 

TABLE  OF   ABBREVIATIONS 

USED  IN  BUSINESS—  (continmd) 

Messrs. 

.  Messieurs  i 

Gentlemen ; 

rec't      .     .  receipt 

Sirs 

rm.  .     . 

.  ream 

mi.    .     . 

.  mile 

Rm.(orM.)  Reich  smark;  Mark 

min. 

.  minute 

s. 

.  shilling;  shillings 

mo.   .     . 

.  month 

S.     .     . 

.  south ;  sales 

mortg.  . 

.  mortgage 

sec.  . 

.  second 

Mr.    .     . 

.  Mister 

sec'y 

.  secretary 

Mrs.       . 

.  Mistress 

Sept. 

.  September 

N.      . 

.  North 

set.  .    . 

.  settlement 

no.     . 

.  number 

ship.     . 

.  shipment 

Nov. 

.  November 

shipt. 

.  shipped 

Oct. 

.  October 

sig.  .     . 

.  signed;  signature 

O.K. 

.  all  correct 

sq.  ch.    . 

.  square  chain 

oz.     . 

.  ounce 

sq.  ft. 

.  square  foot 

p.       . 

•  page 

sq.  mi. 

.  square  mile 

pay't 

.  payment 

sq.rd. 

.  square  rod 

pc.      . 

.     .  piece 

sq.  yd. 

.  square  yard 

pd.     . 

.     .  paid 

stk. 

.  stock 

per     . 

.  by ;  by  the 

sund. 

.  sundries 

per  cent 

.  per  centum ; 

by  the  hun- 

.      T.     . 

.     .  ton 

dred 

tb.    . 

.     .  tub 

pfd.    . 

.  preferred 

Tp. ;  Twp.   township;  townships 

pk.     . 

.  peck;  pecks 

tr.;  trans.  .  transfer 

pkg.  . 

.     .  package 

treas.      .     .  treasurer;  treasury 

pp.     . 

.  pages 

ult.  . 

.  last  month 

pr.      . 

.  pair 

via   . 

.    .  by  way  of 

prox. . 

-     .  the  following  month 

viz.  . 

.  namely;  to  wit 

pt.       . 

.     .  pint 

vol.  . 

.  volume 

pwt.  . 

.     .  pennyweight 

wk.  . 

.  week 

qr.      . 

.     .  quire 

wt.   . 

.  weight;  weigh 

qt.       . 

.     .  quart 

yd.  . 

.  yard 

rd.      . 

.     .  rod 

yr.  . 

.  year 

rec'd  . 

.     .  received 

TABLE  OF  SYMBOLS 

a/c     .  I 

iccount 

c/o      .  care  of 

a/s 

account  sales 

^      .     .  cent 

+    .     . 

addition 

V      .     .  check  mark ;  correct 

(     )     . 

aggregation 

°      .     .  degree 

&     .     . 

and 

-f-     .     .  division 



and  so  on 

$      .     .  dollar;  dollars 

@     .      .   5 

it ;  each  ;  to 

=      .       .   € 

jqual;  equals 

APPENDIX 

TABLE  OF   SYMBOLS - 

—  (continued) 

foot;  feet;  minutes                       o/d 

.  on  demand 

fourths  (written  as  exponents,     fo 

,  per  cent 

thus,  31  =  31)                              £ 

.     .  pounds  sterling 

greater  than                                    : 

.  ratio 

hundred                                           •.•   . 

.  since 

inch;  inches;  seconds                   —   . 

.  subtraction 

less  than                                           .-.  . 

.  therefore 

multiplication                                 M 

.  thousand 

if  written  before  figures,  means 

number;     if    written   after 

figures,  means  pounds 

481 


INDEX 


Abbreviations,  94,  478. 
Acceptance,  300. 
Accounts,  245. 

cash,  245. 

personal,  245. 

receivable  and  payable,  247. 
Account  sales,  452. 
Accuracy,  2,  12,  17,  26,  40. 
Accurate  interest,  269. 
Acre,  94. 
Acute  angle,  112. 
Adding  machine,  47. 
Addition,  2. 

checking,  12. 

column,  4. 

dictation,  8. 

grouping,  5. 

horizontal,  8. 

of  common  fractions,  61,  69. 

of  decimals,  74. 

of  denominate  numbers,  99. 

standards  in,  8. 
Ad  Valorem,  357,  359. 
Advertising,  327,  329. 
Agent,  307,  339. 
Aliquot  parts,  85. 

division  by,  86. 

multiplication  by,  85. 
Altitude,  114. 
Amount,  257. 
Angle,  112. 

Apothecaries'  Weight,  477. 
Appendix,  476. 
Approximate  results,  80. 
Arc,  114. 
Are,  106. 
Area,  114. 

of  circle,  117. 

of  cylinder,  132. 

of  parallelogram,  115. 

of  rectangle,  114. 

of  sphere,  133. 

of  triangle,  115. 


Assessed  value,  346. 
Assessments,  385. 
Assessor,  346. 
Average,  48. 

per  cent  of,  172. 
Avoirdupois  weight,  95,  477. 

Bank, 

discount,  291. 

savings,  282. 
Bank  drafts,  217. 
Bankers'  bills,  236. 
Bankruptcy,  378. 
Base,  114. 

Base  for  percentage,  154,  162. 
Bill  of  exchange,  236. 
Bills,  collecting,  225. 
Blank  form,  ruling,  9. 
Blank  indorsements,  209. 
Board  foot,  135. 
Board  measure,  135. 
Bonds,  394. 
Broker,  388. 
Bushel,  133,  477. 
Business  terms,  478. 
Buying  and  seUing,  176. 
Buying  expenses,  256,  398. 
Buying  stock,  388. 

Canceling  policies,  342. 

Cancellation,  56. 

Carpeting,  129. 

Cash  book,  464. 

Cash  discount,  183. 

Casting  out  nines,  12,  26. 

Certificate  of  stock,  383. 

Certified  check,  216. 

Change,  206. 

Check,  207,  241. 

Checkbook,  210. 

Checking  results,  12,  17,  26,  40,  329. 

Cu-cle,  113. 

Circle  graph,  144. 


483 


484 


INDEX 


Circular  measure,  476. 
Circumference,  116. 
Classifications,  317,  320. 
Clearing  house,  212. 
Collecting  biUs,  225. 
Column  addition,  6. 
Commercial  bills,  237. 
Commercial  discount,  183. 
Commercial  drafts,  227. 
Commission,  307,  452. 
Common  denominator,  61. 
Common  divisor,  57. 
Common  fraction,  59,  79. 
Common  stock,  386. 
Complement,  20. 
Compound  interest,  279. 
Compound  interest  table,  280. 
Computing  machines,  47. 
Consignments,  452. 
Contract  purchases,  288. 
Cord,  132. 

Corporations,  354,  381. 
Cost  book,  416. 
Costs,  factory,  421. 
Courtis  standards,  8. 
Credit,  letters  of,  241. 
Credit  memorandum,  177. 
Cubic  measure,  95. 
Customs  duties,  357. 
CyUnder,  132. 

Day  rate,  303. 
Decimals,  73. 

addition  of,  74. 

division  of,  77. 

multiplication  of,  76. 

reading  of,  73. 

reduction  of,  79. 

subtraction  of,  75. 

writing  of,  73. 
Decrease,  per  cent  of,  168. 
Denominate  numbers,  94,  476. 

addition  of,  99. 

division  of,  101. 

multiplication  of,  101. 

reduction  of,  97,  98. 

subtraction  of,  100. 
Denominator,  59,  61. 
Departments,  profitable,  411. 
Deposit,  207. 
Deposit  slip,  207. 


Depositors'  ledger,  211. 
Depreciation,  323. 
Diagonal,  113. 
Diameter,  114. 
Dictation,  8. 
Differential  rate,  305. 
Discount,  183,  291. 

bank,  291. 

cash,  183. 

fluctuation,  191. 

period,  293,  296. 

quantity,  190. 

series,  189,  192. 

trade,  186. 
Discounting  paper,  291. 
Dividends,  384,  461. 
Divisibility,  tests  of,  55. 
Division,  39. 

aliquot  parts,  86,  91. 

checking,  40. 

long,  40. 

of  decimals,  77. 

of  denominate  numbers,  101. 
Division  of  fractions,  66. 
Divisor,  57. 

Documentary  bill,  238. 
Domestic  mail,  311. 
Dozen,  96. 
Drafts,  217,  227. 

commercial,  227. 
Drawee,  208. 
Drawer,  208,  227. 
Drawings,  137. 
Drawing  to  scale,  138. 
Drill  table,  2,  16,  24,  43. 
Dry  measure,  95. 
Duties, 

ad  valorem,  357,  359. 

specific,  357,  359. 

Efficient  management,  403. 

Eleven,  multiplication  by,  32. 

Endorsement  {see  Indorsement). 

English  money,  96. 

Equilateral,  113. 

Exchange,  215,  235,  239,  240. 

Expenses, 

buying,  256. 

selling,  398. 
Express  money  order,  222. 
Express  rates,  320. 


INDEX 


485 


Factoring,  56. 
Factors  and  multiples,  55. 
Factory  costs,  421. 
Farm  lands,  119,  122. 
Farm  records,  464. 
Fathom,  476. 
Fees,  221. 

Finding  the  percentage,  155. 
Firm,  368. 
Floor  plan,  137. 
Fluctuation  discounts,  191. 
Foot,  abbreviation  for,  94. 
Foreign  coins,  96,  97,  233,  234. 
Foreign  exchange,  235. 
Foreign  postage,  315. 
Fractions,  59. 

addition  of,  61,  69. 

decimal,  73. 

division,  66. 

improper,  59,  60. 

lowest  terms,  59. 

multipHcation  of,  65. 

proper,  59. 

reduction  of,  59,  60,  79. 

subtraction  of,  63,  70. 

terms,  59. 
Franc,  97. 
Freight  rates,  316. 
French  money,  97. 
Fundamental  processes,  2. 

German  money,  97. 

Gothic  pitch,  128. 

Gram,  103. 

Graphic  representations,  137. 

Graphs,  kinds  of,  137. 

Greatest  common  divisor,  57. 

Grocery  orders,  179. 

Gross,  96. 

Gross  sales,  407. 

Gross  trading  profit,  255. 

Grouping,  in  addition,  5. 

Hand,  94. 

Horizontal  addition,  8. 
Hour  rate,  303. 
Hypotenuse,  113,  125. 

Improper  fractions,  59,  60. 
Inch,  abbreviation  for,  94. 
Income  tax,  351. 


Increase,  per  cent  of,  166. 
Indorsement,  208,  209. 
Insolvency,  362,  378. 
Installment  payments,  288. 
Insurance,  333. 

fire,  333. 

life,  458. 

of  parcels,  313. 
Interchanging   principal   and 

262. 
Interest,  257. 

accurate,  269. 

compound,  279. 

on  savings  accounts,  283. 

periodic,  272. 

simple,  257. 

six  per  cent,  258. 

tables,  280. 

terms,  257. 
Inventory,  249,  252. 
Invoice,  176. 
Isosceles,  113. 

Joint  and  several  note,  258. 
Judgment  note,  258. 

Key,  201,  204. 
Knot,  94,  476. 

Land  measure,  94. 

Lapses,  462. 

Least  common  multiple,  57. 

Letters  of  credit,  241. 

Liabilities,  362. 

Life  insurance,  458. 

Linear  measure,  94. 

Link,  476. 

List  price,  183. 

Liter,  103. 

Long  division,  40. 

Long  measure,  94. 

Long  ton,  95. 

Losses,  settlement  of,  340. 

Lowest  terms,  59. 

Machine  rate  method,  430. 
Magazine,  328. 
Mark,  97. 
Marking  cost,  398. 
Marking  goods,  201. 


time, 


486 


INDEX 


Maturity,  291,  294,  394. 

of  drafts,  230. 

of  negotiable  paper,  291,  294. 
Maximum,  per  cent  of,  171. 
Measures,  94. 

apothecaries',  478. 

avoirdupois,  95. 

capacity,  95. 

comparison  of,  109. 

cord,  96. 

counting,  96. 

cubic,  95. 

dry,  95. 

linear,  94. 

liquid,  95. 

long,  94. 

money,  96. 

square,  94. 

time,  96. 

troy,  476,  477. 

weight,  95. 
Merchants'  rule,  276. 
Meter,  103. 
Metric  system,  103. 
Mixed  numbers,  59,  60,  63,  64,  71. 
Money,  96,  233. 

English,  96. 

French,  97. 

German,  97. 

United  States,  96. 
Money  order,  221,  235. 

express,  222. 

post  office,  221. 

telegraph,  223. 
Multiple,  57. 
Multiplicand,  89. 
Multiplication,  24. 

by  aliquot  parts,  85,  88. 

checking,  26. 

common  fractions,  65. 

decimals,  76. 

denominate  numbers,  101. 

short  methods,  29. 
Multiplier,  89. 

Net  profit,  255,  398. 
Newspapers,  327. 
Nines,  casting  out,  12,  26. 
Normal  tax,  351. 
Notes,  257. 

discounting,  291. 


payable,  363. 

receivable,  363. 
Numbers, 

denominate,  94. 

prime,  55. 
Numerator,  59. 

Obtuse  angle,  112. 
Order,  221. 

express,  222. 

postal,  221,  235.; 

telegraph,  223. 
Overhead  expenses,  411,  421. 

Painting,  129. 
Papering,  129. 
Paper  measure,  477. 
Parallelogram,  113. 
Parcel  post,  312. 
Partial  payments,  274. 
Partnership,  368. 
Party  drafts,  227. 
Payee,  227. 

Paying  for  goods,  206. 
Pay  roll  slips,  309. 
Pence,  96. 
Per  cent, 

of  average,  172. 

of  decrease,  168. 

of  increase,  167. 

of  maximum,  171. 
Percentage,  152. 

to  find  base,  162. 

to  find  percentage,  155. 

to  find  rate,  158. 
Perch,  95. 
Perimeter,  113. 

Period,  of  discount,  291,  293,  296. 
Periodic  interest,  272. 
Periodic  inventory,  249. 
Perpendicular,  112. 
Perpetual  inventory,  252. 
Personal  accounts,  245. 
Personal  property,  346. 
Piecework,  304. 
Pitch  of  roof,  128. 
Plastering,  129. 
Policy,  333,  342,  458. 
Postage, 

domestic,  311. 

foreign,  315. 


INDEX 


487 


Postal  money  order,  235. 
Postal  savings  banks,  286. 
Preferred  stock,  386. 
Prefixes,  metric  system,  103,  104. 
Premium,  335,  385. 
Price,  list,  183. 
Prime  factor,  55. 
Prime  number,  55. 
Principal,  257,  271,  307. 
Prism,  130. 
Proceeds  of  note,  291. 
Profitable  departments,  411. 
Profit,  gross  trading,  255. 
Profit,  net,  255. 
Promissory  note,  257. 
Proper  fraction,  59. 
Property  insurance,  333. 
Property  tax,  345. 
Proprietorship,  individual,  362. 
Prorating  expenses,  411,  425. 
Purchases  book,  196. 

Quadrilateral,  113. 
Qualified  indorsement,  209. 
Quantity  discounts,  190. 
Quotation, 

rates  of  exchange,  240. 
Quotient,  41. 

Radius,  114. 

Rate,  154,  158. 

Rate,  day  or  hour,  303. 

Rate,  differential,  305. 

Rate  of  discount,  183. 

Rate  of  exchange,  239. 

Rate  of  interest,  271. 

Rates,  express,  320. 

Rates,  freight,  316. 

Rates  of  insurance,  335,  459. 

Rates,  parcel  post,  314. 

postage,  221. 
Rate,  tax,  346. 
Reading  of  decimals,  73. 
Records,  farm,  464. 
Rectangle,  113. 
Rectilinear  figures,  112. 
Reduction,  59,  60,  62,  97,  98. 
Registry,  313. 
Repeater,  201. 

Resources,  statement  of,  362. 
Right  angle,  112,  125. 


Right  triangle,  125. 
Roofing,  127. 

Sales  book,  197. 
Sales  manager,  439. 
Sales,  recording,  438. 
Sales,  sheet,  438. 
Salvage,  340. 
Savings  accounts,  282. 
Savings  banks,  282,  286. 
Scale,  determining,  141. 

drawing  to,  138. 
Scalene,  113. 
SeUing,  176. 
SeUing  expenses,  398. 
Series,  discount,  189,  192. 
Sharing  profits,  371. 
Shilling,  96. 
Short  division,  39. 
Short  methods,  29,  69,  85. 
Sight  draft,  227. 
Simple  interest,  257. 
Six  per  cent  method,  258. 
Sixty  day  method,  258. 
SoHds,  130. 
Specific,  357,  359. 
Speed  tests,  2,  16,  24,  43. 
Square,  94,  113. 
Square  measure,  94. 
Square  root,  122. 
Standard  bushels,  477. 
State  taxes,  345. 
Statistics,  how  to  enter,  9. 
Stock  record,  252. 
Stocks,  381,  386. 
Subtraction,  16. 

checking,  17. 

complement  method,  19. 

of  common  fractions,  63,  70. 

of  decimals,  75. 

of  denominate  numbers,  100. 
Subtrahend,  17. 
Surface,  112. 
Surface  measure,  94. 
Surplus,  384. 
Surveyors'  measure,  476. 
Symbols  in  business,  479,  480. 

Tables, 

abbreviations  in  business,  478. 
aliquot  parts,  88. 


488 


INDEX 


Tables, 

apothecaries'  weight,  478. 

avoirdupois  weight,  95. 

compound  interest,  280. 

counting,  96. 

cubic  measure,  95. 

English  money,  96. 

express,  321. 

French  money,  97. 

German  money,  97. 

interest,  280. 

linear  measure,  94, 

liquid  measure,  95. 

parcel  post,  314. 

symbols,  480. 

troy  weight,  476,  477. 
Tariff,  freight,  318. 
Tax,  income,  351. 
Taxation,  345,  348. 
Telegraph  money  orders,  223. 
Term  of  discount,  183. 
Terms  of  fractions,  59. 
Terms  of  percentage,  154. 
Tests  of  divisibility,  55. 
Time,  96. 

draft,  227. 
Trade  discount,  186. 
Trade  profit,  255. 
Travelers'  checks,  241. 
Triangle,  113. 


Troy  weight,  476,  477. 
Turnovers,  408. 
Two  party  draft,  227. 

Underwriter,  333. 
United  States  money,  96. 
United  States  rule,  274. 
Unit  fractions,  69. 
Units  of  measure,  94. 

Value,  of  foreign  coins,  96,  97. 
Value,  of  note,  291. 
Vertex,  112. 
Volume,  95. 

of  cylinder,  132. 

of  prism,  131. 

of  sphere,  133. 

Weight,  476,  477. 

apothecaries',  477. 

avoirdupois,  95. 

comparison  of,  109. 

miscellaneous,  477. 

troy,  476,  477. 
Withdrawals,  207. 
Wood  measure,  96. 
Writing  decimals,  73. 

Zones,  parcel  post,  312. 


^'B  3091 


f 


402220 


UNIVERSITY  OF  CALIFORNIA  UBRARY 


